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    Wyświetlanie 1-46 z 46
    Tytuł:
    Existence and solution sets of impulsive functional differential inclusions with multiple delay
    Autorzy:
    Helal, M.
    Ouahab, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/256052.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    impulsive functional differential inclusions
    decomposable set
    parameter differential inclusions
    AR-set
    control theory
    Opis:
    In this paper, we present some existence results of solutions and study the topological structure of solution sets for the following first-order impulsive neutral functional differential inclusions with initial condition: [formula] where J : = [0; b] and 0 = t0 < t1 < ... < tm < tm+1 = b (m ∈ N*), F is a set-valued map and g is single map. The functions Ik characterize the jump of the solutions at impulse points tk (k = 1, ... m). Our existence result relies on a nonlinear alternative for compact u.s.c. maps. Then, we present some existence results and investigate the compactness of solution sets, some regularity of operator solutions and absolute retract (in short AR). The continuous dependence of solutions on parameters in the convex case is also examined. Applications to a problem from control theory are provided.
    Źródło:
    Opuscula Mathematica; 2012, 32, 2; 249-283
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some averaging results for ordinary differential inclusions
    Autorzy:
    Bourada, Amel
    Guen, Rahma
    Lakrib, Mustapha
    Yadi, Karim
    Powiązania:
    https://bibliotekanauki.pl/articles/729511.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    ordinary differential inclusions
    averaging method
    Opis:
    We consider ordinary differential inclusions and we state and discuss some averaging results for these inclusions. Our results are proved under weaker conditions than the results in the literature.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2015, 35, 1; 47-63
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Viability theory: an applied mathematics tool for achieving dynamic systems sustainability
    Autorzy:
    Krawczyk, Jacek B.
    Pharo, Alastair S.
    Powiązania:
    https://bibliotekanauki.pl/articles/748128.pdf
    Data publikacji:
    2013
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    viability theory, differential inclusions, sustainability
    Opis:
     Sustainability is considered an issue of paramount importance; yet scientists andpoliticians still seek to understand what it means, practically and conceptually, tobe sustainable. This paper's aim is to introduce viability theory, a relativelyyoung branch of continuous mathematics which provides a conceptual frameworkthat is very well suited to sustainability problems.  In particular, viability theory can be used toanswer important questions about the sustainability of systems, including thosestudied in macroeconomics, and can be used to determine sustainable policies fortheir management.  The principal analytical tool of viability theory is theviability kernel which is the set of all state-space points such that it is possible for evolutions starting from each of those points to remain within the system's predetermined constraints indefinitely. Although, in some circumstances,  kernel determinationcan be performed analytically,  most practical results in viability theory rely on graphical approximations of viability kernels,which for nonlinear and high-dimensional problems can only be approached numerically.This paper provides an outline of the coreconcepts of viability theory and an overview of the numerical approachesavailable for computing approximate viability kernels.  \vikaasa{}, aspecialised software application developed by the authors and designed tocompute such approximate viability kernels is presented along-side examples ofviability theory in action in the spheres of bio-economics and macroeconomics.
    Źródło:
    Mathematica Applicanda; 2013, 41, 1
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A constructive method for solving stabilization problems
    Autorzy:
    Azhmyakov, Vadim
    Powiązania:
    https://bibliotekanauki.pl/articles/729257.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    differential inclusions
    difference inclusions
    Lyapunov function
    asymptotic stability
    Opis:
    The problem of asymptotic stabilization for a class of differential inclusions is considered. The problem of choosing the Lyapunov functions from the parametric class of polynomials for differential inclusions is reduced to that of searching saddle points of a suitable function. A numerical algorithm is used for this purpose. All the results thus obtained can be extended to cover the discrete systems described by difference inclusions.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2000, 20, 1; 51-62
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability theorem for nonlinear dynamical systems
    Autorzy:
    Kisielewicz, Michał
    Powiązania:
    https://bibliotekanauki.pl/articles/729548.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    differential equation
    differential inclusions
    controllability
    boundary value problem
    Opis:
    Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2002, 22, 2; 225-232
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and Topological Properties of Solution Sets for Differential Inclusions with Delay
    Autorzy:
    Gomaa, Adel Mahmoud
    Powiązania:
    https://bibliotekanauki.pl/articles/746625.pdf
    Data publikacji:
    2008
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Differential inclusions
    mutifunctions
    measures of noncompactness
    delay
    Opis:
    We consider the problem \(\dot{x}(t) \in A(t)x(t) + F (t, θ_t x))\) a.e. on \([0, b]\), \(x = \kappa\) on \([-d, 0]\) in a Banach space \(E\), where \(\kappa\) belongs to the Banach space, \(C_E ([-d, 0])\), of all continuous functions from \([-d, 0]\) into \(E\). A multifunction \(F\) from \([0, b] \times C_E ([-d, 0])\) into the set, \(P_{f_c} (E)\), of all nonempty closed convex subsets of \(E\) is weakly sequentially hemi-continuous, \(θ_t x(s) = x(t + s)\) for all \(s \in [-d, 0]\) and \(\{A(t) : 0 \leq t \leq b\}\) is a family of densely defined closed linear operators generating a continuous evolution operator \(S(t, s)\). Under a generalization of the compactness assumptions, we prove an existence result and give some topological properties of our solution sets that generalizes earlier theorems by Papageorgiou, Rolewicz, Deimling, Frankowska and Cichoń.
    Źródło:
    Commentationes Mathematicae; 2008, 48, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stochastic differential inclusions of Langevin type on Riemannian manifolds
    Autorzy:
    Gliklikh, Yuri
    Obukhovskiĭ, Andrei
    Powiązania:
    https://bibliotekanauki.pl/articles/729326.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    stochastic differential inclusions
    Langevin equation
    Riemannian manifolds
    Opis:
    We introduce and investigate a set-valued analogue of classical Langevin equation on a Riemannian manifold that may arise as a description of some physical processes (e.g., the motion of the physical Brownian particle) on non-linear configuration space under discontinuous forces or forces with control. Several existence theorems are proved.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 2; 173-190
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A viability result for nonconvex semilinear functional differential inclusions
    Autorzy:
    Lupulescu, Vasile
    Necula, Mihai
    Powiązania:
    https://bibliotekanauki.pl/articles/729593.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    viability
    invariance
    tangency condition
    semilinear differential inclusions
    Opis:
    We establish some sufficient conditions in order that a given locally closed subset of a separable Banach space be a viable domain for a semilinear functional differential inclusion, using a tangency condition involving a semigroup generated by a linear operator.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2005, 25, 1; 109-128
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the existence of viable solutions for a class of second order differential inclusions
    Autorzy:
    Cernea, Aurelian
    Powiązania:
    https://bibliotekanauki.pl/articles/729526.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    viable solutions
    ϕ-monotone operators
    differential inclusions
    Opis:
    We prove the existence of viable solutions to the Cauchy problem x'' ∈ F(x,x'), x(0) = x₀, x'(0) = y₀, where F is a set-valued map defined on a locally compact set $M ⊂ R^{2n}$, contained in the Fréchet subdifferential of a ϕ-convex function of order two.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2002, 22, 1; 67-78
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the theorem of Filippov-Pliś and some applications
    Autorzy:
    Donchev, T.
    Farkhi, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/970906.pdf
    Data publikacji:
    2009
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    differential inclusions
    one-sided
    Lipschitz
    Filippov
    Plis
    Opis:
    In the paper some known and new extensions of the famous theorem of Filippov (1967) and a theorem of Plis (1965) for differential inclusions are presented. We replace the Lipschitz condition on the set-valued map in the right-hand side by a weaker onesided Lipschitz (OSL), one-sided Kamke (OSK) or a continuity-like condition (CLC). We prove new Filippov-type theorems for singularly perturbed and evolution inclusions with OSL right-hand sides. In the CLC case we obtain two extended theorems, one of which implies directly the relaxation theorem. We obtain also a theorem in Banach spaces for OSK multifunctions. Some applications to exponential formulae are surveyed.
    Źródło:
    Control and Cybernetics; 2009, 38, 4A; 1251-1271
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some optimal control problems for partial differential inclusions
    Autorzy:
    Kisielewicz, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255397.pdf
    Data publikacji:
    2008
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    partial differential inclusions
    diffusion processes
    existence theorems
    Opis:
    Partial differential inclusions are considered. In particular, basing on diffusions properties of weak solutions to stochastic differential inclusions, some existence theorems and some properties of solutions to partial differential inclusions are given.
    Źródło:
    Opuscula Mathematica; 2008, 28, 4; 507-516
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hybrid fractional integro-differential inclusions
    Autorzy:
    Ntouyas, Sotiris
    Laoprasittichok, Sorasak
    Tariboon, Jessada
    Powiązania:
    https://bibliotekanauki.pl/articles/729621.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fractional differential equations
    hybrid differential inclusions
    fixed point theorems
    Opis:
    In this paper we study an existence result for initial value problems for hybrid fractional integro-differential inclusions. A hybrid fixed point theorem for a sum of three operators due to Dhage is used. An example illustrating the obtained result is also presented.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2015, 35, 2; 151-164
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On differential equations and inclusions with mean derivatives on a compact manifold
    Autorzy:
    Azarina, S.
    Gliklikh, Yu.
    Powiązania:
    https://bibliotekanauki.pl/articles/729459.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    mean derivatives
    differential inclusions
    stochastic processes on manifolds
    Opis:
    We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 385-397
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence theorems for a semilinear elliptic boundary value problem
    Autorzy:
    Marano, Salvatore
    Powiązania:
    https://bibliotekanauki.pl/articles/1311657.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    elliptic differential inclusions
    semilinear elliptic equations
    strong solutions
    Opis:
    Let Ω be a bounded domain in $ℝ^n$, n ≥ 3, with a smooth boundary ∂Ω; let L be a linear, second order, elliptic operator; let f and g be two real-valued functions defined on Ω × ℝ such that f(x,z) ≤ g(x,z) for almost every x ∈ Ω and every z ∈ ℝ. In this paper we prove that, under suitable assumptions, the problem { f(x,u) ≤ Lu ≤ g(x,u)   in Ω, u = 0     on ∂Ω, has at least one strong solution $u ∈ W^{2,p}(Ω) ∩ W^{1,p}_0(Ω). Next, we present some remarkable special cases.
    Źródło:
    Annales Polonici Mathematici; 1994-1995, 60, 1; 57-67
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On controllability for fractional differential inclusions in Banach spaces
    Autorzy:
    Wang, J.
    Li, X.
    Wei, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/256046.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    controllability
    fractional differential inclusions
    Bohnenblust-Karlin's fixed point theorem
    Opis:
    In this paper, we investigate the controllability for systems governed by fractional differential inclusions in Banach spaces. The techniques rely on fractional calculus, multivalue mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem.
    Źródło:
    Opuscula Mathematica; 2012, 32, 2; 341-356
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence results for delay second order differential inclusions
    Autorzy:
    Azzam-Laouir, Dalila
    Haddad, Tahar
    Powiązania:
    https://bibliotekanauki.pl/articles/729461.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    boundary-value problems
    delay differential inclusions
    fixed point
    retract
    Opis:
    In this paper, some fixed point principle is applied to prove the existence of solutions for delay second order differential inclusions with three-point boundary conditions in the context of a separable Banach space. A topological property of the solutions set is also established.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 133-146
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An existence theorem for set differential inclusions in a semilinear metric space
    Autorzy:
    De Blasi, F. S.
    Lakshmikantham, V.
    Bhaskar, T. G.
    Powiązania:
    https://bibliotekanauki.pl/articles/970280.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    approximate continuous selections
    Cauchy problem
    set differential inclusions
    Hukuhara derivative
    Opis:
    Using the notion of continuous approximate selections, we establish an existence theorem for set differential inclusions in a semi-linear metric space.
    Źródło:
    Control and Cybernetics; 2007, 36, 3; 571-582
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A deterministic approach to the Skorokhod problem
    Autorzy:
    Bettiol, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/970021.pdf
    Data publikacji:
    2006
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Skorokhod problem
    reflection on the boundary
    differential inclusions
    differential games
    value function
    Opis:
    We prove an existence and uniqueness result for the solutions to the Skorokhod problem on uniformly prox-regular sets through a deterministic approach. This result can be applied in order to investigate some regularity properties of the value function for differential games with reflection on the boundary.
    Źródło:
    Control and Cybernetics; 2006, 35, 4; 787-802
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of solutions for second order stochastic differential inclusions in Hilbert spaces
    Autorzy:
    Balasubramaniam, P.
    Ntouyas, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/729455.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    existence
    multivalued map
    stochastic differential inclusions
    fixed point
    Hilbert space
    Opis:
    In this paper, sufficient conditions are given for the existence of solutions for a class of second order stochastic differential inclusions in Hilbert space with the help of Leray-Schauder Nonlinear Alternative.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 365-384
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces
    Autorzy:
    Gudovich, Anastasie
    Kamenski, Mikhail
    Nistri, Paolo
    Powiązania:
    https://bibliotekanauki.pl/articles/729318.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    singular perturbations
    differential inclusions
    analytic semigroups
    multivalued compact operators
    Lipschitz selections
    Opis:
    We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset $Z_L(ε)$ of the solution set of the singularly perturbed system. This subset is the set of the Hölder continuous solutions defined in [0,d], d > 0 with prescribed exponent and constant L. We show that $Z_L(ε)$ is uppersemicontinuous at ε = 0 in the C[0,d]×C[δ,d] topology for any δ ∈ (0,d].
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 2; 207-234
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal control of impulsive stochastic evolution inclusions
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729552.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    impulsive perturbations
    C₀-semigroups
    stochastic systems
    differential inclusions
    vector measures
    optimal controls
    Opis:
    In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2002, 22, 2; 155-184
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence results for nonlocal boundary value problems for fractional differential equations and inclusions with fractional integral boundary conditions
    Autorzy:
    Ntouyas, Sotiris
    Powiązania:
    https://bibliotekanauki.pl/articles/729316.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fractional differential equations
    fractional differential inclusions
    nonlocal boundary conditions
    fixed point theorems
    Leray-Schauder degree
    Opis:
    This paper studies a new class of nonlocal boundary value problems of nonlinear differential equations and inclusions of fractional order with fractional integral boundary conditions. Some new existence results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also discussed.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 1; 17-39
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions
    Autorzy:
    Ahmad, Bashir
    Ntouyas, Sotiris
    Powiązania:
    https://bibliotekanauki.pl/articles/729350.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fractional differential inclusions
    anti-periodic
    integral boundary conditions
    existence
    fixed point theorems
    Opis:
    This article studies a boundary value problem of nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions. Some existence results are obtained via fixed point theorems. The cases of convex-valued and nonconvex-valued right hand sides are considered. Several new results appear as a special case of the results of this paper.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2012, 32, 1; 45-62
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An existence theorem for fractional hybrid differential inclusions of Hadamard type
    Autorzy:
    Ahmad, Bashir
    Ntouyas, Sotiris
    Powiązania:
    https://bibliotekanauki.pl/articles/729503.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Hadamard fractional derivative
    hybrid differential inclusions
    Diriclet boundary conditions
    existence
    fixed point
    Opis:
    This paper studies the existence of solutions for fractional hybrid differential inclusions of Hadamard type by using a fixed point theorem due to Dhage. The main result is illustrated with the aid of an example.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 2; 207-218
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Impulsive perturbation of C₀-semigroups and stochastic evolution inclusions
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729564.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    impulsive perturbations
    C₀-semigroups
    stochastic systems
    differential inclusions
    vector measures
    impulsive controls
    Opis:
    In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions. We prove existence of solutions and study properties of the solution set. It is also indicated how these results can be used in the study of control systems driven by vector measures.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2002, 22, 1; 125-149
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability of evolution equations and inclusions driven by vector measures
    Autorzy:
    Ahmed, N.U.
    Powiązania:
    https://bibliotekanauki.pl/articles/729615.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    controlability
    impulsive systems
    differential inclusions
    Hilbert spaces
    vector valued measures
    C₀ semigroups
    Opis:
    In this paper, we consider the question of controllability of a class of linear and semilinear evolution equations on Hilbert space with measures as controls. We present necessary and sufficient conditions for weak and exact (strong) controllability of a linear system. Using this result we prove that exact controllability of the linear system implies exact controllability of a perturbed semilinear system. Controllability problem for the semilinear system is formulated as a fixed point problem on the space of vector measures and is concluded controllability from the existence of a fixed point. Our results cover impulsive controls as well as regular controls.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2004, 24, 1; 49-72
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Forward invariant sets, homogeneity and small-time local controllability
    Autorzy:
    Krastanov, Mikhail
    Powiązania:
    https://bibliotekanauki.pl/articles/1359675.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    small-time local controllability
    forward invariant sets
    differential inclusions
    homogeneous control systems
    Opis:
    The property of forward invariance of a subset of $R^n$ with respect to a differential inclusion is characterized by using the notion of a perpendicular to a set. The obtained results are applied for investigating the dependence of the small-time local controllability of a homogeneous control system on parameters.
    Źródło:
    Banach Center Publications; 1995, 32, 1; 287-300
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence results for impulsive semilinear fractional differential inclusions with delay in Banach spaces
    Autorzy:
    Hammouche, Hadda
    Guerbati, Kaddour
    Benchohra, Mouffak
    Abada, Nadjat
    Powiązania:
    https://bibliotekanauki.pl/articles/729312.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fractional calculus
    caputo fractional derivative
    multivalued map
    differential inclusions
    mild solution
    fixed point
    Opis:
    In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 2; 149-170
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weak solutions of stochastic differential inclusions and their compactness
    Autorzy:
    Michta, Mariusz
    Powiązania:
    https://bibliotekanauki.pl/articles/729384.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    semimartingale
    stochastic differential inclusions
    weak solutions
    martingale problem
    weak convergence of probability measures
    Opis:
    In this paper, we consider weak solutions to stochastic inclusions driven by a semimartingale and a martingale problem formulated for such inclusions. Using this we analyze compactness of the set of solutions. The paper extends some earlier results known for stochastic differential inclusions driven by a diffusion process.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2009, 29, 1; 91-106
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds
    Autorzy:
    Gliklikh, Yuri
    Obukhovski, Andrei
    Powiązania:
    https://bibliotekanauki.pl/articles/729628.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    differential inclusions
    Carathéodory conditions
    velocity hodograph
    Riemannian manifold
    two-point bounadry value problem
    Opis:
    We investigate velocity hodograph inclusions for the case of right-hand sides satisfying upper Carathéodory conditions. As an application we obtain an existence theorem for a boundary value problem for second-order differential inclusions on complete Riemannian manifolds with Carathéodory right-hand sides.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2004, 24, 1; 41-48
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence results for ϕ-Laplacian Dirichlet BVP of differential inclusions with application to control theory
    Autorzy:
    Djebali, Smaïl
    Ouahab, Abdelghani
    Powiązania:
    https://bibliotekanauki.pl/articles/729271.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    differential inclusions
    boundary value problem
    fixed point
    compact
    convex
    nonconvex
    decomposable
    continuous selection
    controllability
    Opis:
    In this paper, we study ϕ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multi-valued right-hand side. The nonlinearity satisfies either a Nagumo-type growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively. Two applications to a problem from control theory are provided.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 1; 23-49
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Delay perturbed evolution problems involving time dependent subdifferential operators
    Autorzy:
    Saïdi, Soumia
    Yarou, Mustapha
    Powiązania:
    https://bibliotekanauki.pl/articles/729544.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Differential inclusions
    subdifferential operator
    Lipschitz functions
    set-valued map
    delay
    perturbation
    absolutely continuous map
    Opis:
    We investigate in the present paper, the existence and uniqueness of solutions for functional differential inclusions involving a subdifferential operator in the infinite dimensional setting. The perturbation which contains the delay is single-valued, separately measurable, and separately Lipschitz. We prove, without any compactness condition, that the problem has one and only one solution.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 1; 61-87
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Boundary value problems for nonlinear fractional differential equations and inclusions with nonlocal and fractional integral boundary conditions
    Autorzy:
    Ntouyas, S. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/254690.pdf
    Data publikacji:
    2013
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fractional differential equations
    fractional differential inclusions
    nonlocal conditions
    fractional integral boundary conditions
    existence
    contraction principle
    nonlinear contraction
    Opis:
    This paper studies the boundary value problem of nonlinear fractional differential equations and inclusions of order q ∈ (1, 2] with nonlocal and integral boundary conditions. Some new existence and uniqueness results are obtained by using fixed point theorems.
    Źródło:
    Opuscula Mathematica; 2013, 33, 1; 117-138
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces
    Autorzy:
    Abada, Nadjat
    Benchohra, Mouffak
    Hammouche, Hadda
    Ouahab, Abdelghani
    Powiązania:
    https://bibliotekanauki.pl/articles/729413.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    semilinear functional differential inclusions
    impulses
    mild solution
    fixed point
    controllability
    extrapolation space
    nondensely defined operator
    Opis:
    In this paper, we use the extrapolation method combined with a recent nonlinear alternative of Leray-Schauder type for multivalued admissible contractions in Fréchet spaces to study the existence of a mild solution for a class of first order semilinear impulsive functional differential inclusions with finite delay, and with operator of nondense domain in original space.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 329-347
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Partially dissipative periodic processes
    Autorzy:
    Andres, Jan
    Górniewicz, Lech
    Lewicka, Marta
    Powiązania:
    https://bibliotekanauki.pl/articles/1358930.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    large-period forced oscillations
    partial dissipativity
    Poincaré translation operator
    fixed point index
    differential inclusions
    Periodic processes
    Opis:
    Further extension of the Levinson transformation theory is performed for partially dissipative periodic processes via the fixed point index. Thus, for example, the periodic problem for differential inclusions can be treated by means of the multivalued Poincaré translation operator. In a certain case, the well-known Ważewski principle can also be generalized in this way, because no transversality is required on the boundary.
    Źródło:
    Banach Center Publications; 1996, 35, 1; 109-118
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and controllability results for semilinear neutral functional differential inclusions with nonlocal conditions
    Autorzy:
    Ntouyas, S.
    O'Regan, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/729421.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    semilinear differential inclusions
    nonlocal conditions
    analytic semigroups
    cosine functions
    integrated semigroups
    fixed point
    nonlinear alternative
    controllability
    Opis:
    In this paper, we prove existence and controllability results for first and second order semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces, with nonlocal conditions. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 213-264
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solution tubes to differential inclusions within a collection of sets
    Autorzy:
    Quincampoix, M.
    Veliov, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/206199.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    estymacja deterministyczna
    system niepewny
    system sterowania
    control systems
    deterministic estimation
    differential inclusions
    reachable sets
    uncertain systems
    Opis:
    This paper develops the theory of solution tubes to differential inclusions (uncertain systems) within a prescribed collection of sets. The notion is defined as a minimal invariant tube with values in the collection. Under certain requirements for the collection we prove existence and Lipschitz-like stability of the solution tubes. The theory is relevant to problems of systems estimation in the context of control or differential games.
    Źródło:
    Control and Cybernetics; 2002, 31, 3; 847-862
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A study of second order differential inclusions with four-point integral boundary conditions
    Autorzy:
    Ahmad, Bashir
    Ntouyas, Sotiris
    Powiązania:
    https://bibliotekanauki.pl/articles/729334.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    differential inclusions
    four-point integral boundary conditions
    existence
    nonlinear alternative of Leray Schauder type
    fixed point theorems
    Opis:
    In this paper, we discuss the existence of solutions for a four-point integral boundary value problem of second order differential inclusions involving convex and non-convex multivalued maps. The existence results are obtained by applying the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 2; 137-156
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Boundary value problems for n-th order differential inclusions with four-point integral boundary conditions
    Autorzy:
    Ahmad, B.
    Ntouyas, S. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/255975.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    differential inclusions
    four-point integral boundary conditions
    existence
    nonlinear alternative of Leray Schauder type
    fixed-point theorems
    Opis:
    In this paper, we discuss the existence of solutions for a four-point integral boundary value problem of n-th order differential inclusions involving convex and non-convex multivalued maps. The existence results are obtained by applying the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.
    Źródło:
    Opuscula Mathematica; 2012, 32, 2; 205-226
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of solutions for a multivalued boundary value problem with non-convex and unbounded right-hand side
    Autorzy:
    Averna, Diego
    Bonanno, Gabriele
    Powiązania:
    https://bibliotekanauki.pl/articles/1294053.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    multivalued differential inclusions
    boundary value problems
    non-convex and unbounded right-hand side
    directional continuous selections
    implicit equations
    Opis:
    Let $F:[a,b] × ℝ^n × ℝ^n → 2^{ℝ^n}$ be a multifunction with possibly non-convex and unbounded values. The main result of this paper (Theorem 1) asserts that, given the multivalued boundary value problem ($P_F$)    {u'' ∈ F(t,u,u'), u(a) = u(b) = ϑ_{ℝ^n}, if an appropriate restriction of the multifunction F has non-empty and closed values and satisfies the lower Scorza Dragoni property and a weak integrable boundedness type condition, then we can substitute the problem ($P_F$) with another one ($P_G$), with a suitable convex right-hand side G, such that every generalized solution of ($P_G$) is also a generalized solution of ($P_F$) (see also Remark 1 and Corollary 1). As a consequence of our results, in conjunction with those in [13] and [18], some existence theorems for multivalued boundary value problems are then presented (see Theorem 2, Corollary 2 and Theorem 3). Finally, some applications are given to the existence of generalized solutions for two implicit boundary value problems (Theorems 4-6).
    Źródło:
    Annales Polonici Mathematici; 1999, 71, 3; 253-271
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional integro-differential inclusions with state-dependent delay
    Autorzy:
    Aissani, Khalida
    Benchohra, Mouffak
    Ezzinbi, Khalil
    Powiązania:
    https://bibliotekanauki.pl/articles/729499.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fractional integro-differential inclusions
    Caputo fractional derivative
    mild solution
    multivalued map
    Bohnenblust-Karlin's fixed point
    state-dependent delay
    Opis:
    In this paper, we establish sufficient conditions for the existence of mild solutions for fractional integro-differential inclusions with state-dependent delay. The techniques rely on fractional calculus, multivalued mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem. Finally, we present an example to illustrate the theory.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 2; 153-167
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Systems of differential inclusions in the absence of maximum principles and growth conditions
    Autorzy:
    Tisdell, Christopher
    Powiązania:
    https://bibliotekanauki.pl/articles/729443.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    boundary value problem
    systems of differential inclusions
    existence of solutions
    a priori bounds
    two-point boundary conditions
    three-point boundary conditions
    Opis:
    This article investigates the existence of solutions to second-order boundary value problems (BVPs) for systems of ordinary differential inclusions. The boundary conditions may involve two or more points. Some new inequalities are presented that guarantee a priori bounds on solutions to the differential inclusion under consideration. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow the treatment of systems of BVPs in the absence of maximum principles and growth conditions. The results are also new for differential equations involving Carathéodory or even continuous right-hand sides.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2006, 26, 1; 129-141
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional order impulsive partial hyperbolic differential inclusions with variable times
    Autorzy:
    Abbas, Saïd
    Benchohra, Mouffak
    Górniewicz, Lech
    Powiązania:
    https://bibliotekanauki.pl/articles/729238.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    impulsive functional differential inclusions
    fractional order
    solution
    left-sided mixed Riemann-Liouville integral
    Caputo fractional-order derivative
    variable times
    fixed point
    Opis:
    This paper deals with the existence of solutions to some classes of partial impulsive hyperbolic differential inclusions with variable times involving the Caputo fractional derivative. Our works will be considered by using the nonlinear alternative of Leray-Schauder type.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 1; 91-114
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Evolution equations in ostensible metric spaces: First-order evolutions of nonsmooth sets with nonlocal terms
    Autorzy:
    Lorenz, Thomas
    Powiązania:
    https://bibliotekanauki.pl/articles/729470.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    mutational equations
    quasidifferential equations
    funnel equations
    nonlocal geometric evolutions
    reachable sets of differential inclusions
    sets of positive erosion
    sets of positive reach
    Opis:
    Similarly to quasidifferential equations of Panasyuk, the so-called mutational equations of Aubin provide a generalization of ordinary differential equations to locally compact metric spaces. Here we present their extension to a nonempty set with a possibly nonsymmetric distance. In spite of lacking any linear structures, a distribution-like approach leads to so-called right-hand forward solutions.
    These extensions are mainly motivated by compact subsets of the Euclidean space whose evolution is determined by the nonlocal properties of both the current set and the normal cones at its topological boundary. Indeed, simple deformations such as isotropic expansions exemplify that topological boundaries do not have to evolve continuously in time and thus Aubin's original concept cannot be applied directly. Here neither regularity assumptions about the boundaries nor the inclusion principle are required. The regularity of compact reachable sets of differential inclusions is studied extensively instead.
    This example of nonlocal set evolutions in the Euclidean space serves as an introductory motivation for extending ordinary differential equations (and evolution equations) beyond the traditional border of vector spaces - and for combining it with other examples in systems.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 15-73
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal control of delay-differential inclusions with multivalued initial conditions in infinite dimensions
    Autorzy:
    Mordukhovich, B. S.
    Wang, D.
    Wang, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/969562.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    discrete approximations
    optimal control
    variational analysis
    endpoint constraints
    delay-differential inclusions
    multivalued initial conditions
    extended Euler-Lagrange formalism
    generalized differentiation
    Banach and Asplund spaces
    necessary optimality conditions
    Opis:
    This paper is devoted to the study of a general class of optimal control problems described by delay-differential inclusions with infinite-dimensional state spaces, endpoints constraints, and multivalued initial conditions. To the best of our knowledge, problems of this type have not been considered in the literature, except for some particular cases when either the state space is finite-dimensional or there is no delay in the dynamics. We develop the method of discrete approximations to derive necessary optimality conditions in the extended Euler-Lagrange form by using advanced tools of variational analysis and generalized differentiation in infinite dimensions. This method consists of the three major parts: (a) constructing a well-posed sequence of discrete-time problems that approximate in an appropriate sense the original continuous-time problem of dynamic optimization; (b) deriving necessary optimality conditions for the approximating discrete-time problems by reducing them to infinite-dimensional problems of mathematical programming and employing then generalized differential calculus; (c) passing finally to the limit in the obtained results for discrete approximations to establish necessary conditions for the given optimal solutions to the original problem. This method is fully realized in the delay-differential systems under consideration.
    Źródło:
    Control and Cybernetics; 2008, 37, 2; 393-428
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal control of constrained delay-differential inclusions with multivalued initial conditions
    Autorzy:
    Mordukhovich, B. S.
    Wang, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/970519.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    aproksymacja dyskretna
    warunek konieczny optymalności
    analiza wariacyjna
    stabilność
    optymalizacja niegładka
    różniczkowanie uogólnione
    delay-differential inclusions
    discrete approximations
    necessary optimality conditions
    variational analysis
    stability
    nonsmooth optimization
    generalized differentiation
    Opis:
    This paper studies a general optimal control problem for nonconvex delay-differential inclusions with endpoint constraints. In contrast to previous publications on this topic, we incorporate time-dependent set constraints on the initial interval, which are specific for systems with delays and provide an additional source for optimization. Our variational analysis is based on well-posed discrete approximations of constrained delay-differential inclusions by a family of time-delayed systems with discrete dynamics and perturbed constraints. Using convergence results for discrete approximations and advanced tools of nonsmooth variational analysis, we derive necessary optimality conditions for constrained delay-differential inclusions in both Euler-Lagrange and Hamiltonian forms involving nonconvex generalized differential constructions for nonsmooth functions, sets, and set-valued mappings.
    Źródło:
    Control and Cybernetics; 2003, 32, 3; 585-609
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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