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    Wyświetlanie 1-24 z 24
    Tytuł:
    An optimal control problem for a fourth-order variational inequality
    Autorzy:
    Khludnev, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1361143.pdf
    Data publikacji:
    1992
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Opis:
    An optimal control problem is considered where the state of the system is described by a variational inequality for the operator w → εΔ²w - φ(‖∇w‖²)Δw. A set of nonnegative functions φ is used as a control region. The problem is shown to have a solution for every fixed ε > 0. Moreover, the solvability of the limit optimal control problem corresponding to ε = 0 is proved. A compactness property of the solutions of the optimal control problems for ε > 0 and their relation with the limit problem are established. This type of operator arises in the theory of nonlinear plates, and the choice of a most suitable function φ is of interest for applications [2]. The problem of control of the function w has been studied in [4] for the operator under consideration, and some statements of this work will be used. Nonstationary problems with analogous operators were analyzed in [6,7]. Some general results on control of second-order variational inequalities can be found in [1]. The first section of this paper deals with the control problem for our fourth-order operator, the second considers a second-order operator, and the third studies the relationship between the solutions of the two problems.
    Źródło:
    Banach Center Publications; 1992, 27, 1; 225-231
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Topology optimization of systems governed by variational inequalities
    Autorzy:
    Myśliński, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/729259.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    variational inequality
    topology optimization
    Opis:
    This paper deals with the formulation of the necessary optimality condition for a topology optimization problem of an elastic body in unilateral contact with a rigid foundation. In the contact problem of Tresca, a given friction is governed by an elliptic variational inequality of the second order. The optimization problem consists in finding such topology of the domain occupied by the body that the normal contact stress along the contact boundary of the body is minimized. The topological derivative of the cost functional is calculated and a necessary optimality condition is formulated. The calculated topological derivative is also used in the numerical algorithm to find a descent direction by inserting voids in the domain occupied by the body. Numerical examples are provided.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 2; 237-252
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical considerations of a hybrid proximal projection algorithm for solving variational inequalities
    Autorzy:
    Jager, Christina
    Powiązania:
    https://bibliotekanauki.pl/articles/729431.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    variational inequality
    proximal point algorithm
    bundle method
    Opis:
    In this paper, some ideas for the numerical realization of the hybrid proximal projection algorithm from Solodov and Svaiter [22] are presented. An example is given which shows that this hybrid algorithm does not generate a Fejér-monotone sequence. Further, a strategy is suggested for the computation of inexact solutions of the auxiliary problems with a certain tolerance. For that purpose, ε-subdifferentials of the auxiliary functions and the bundle trust region method from Schramm and Zowe [20] are used. Finally, some numerical results for non-smooth convex optimization problems are given which compare the hybrid algorithm to the inexact proximal point method from Rockafellar [17].
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 1; 51-69
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Local subdifferentials and multivariational inequalities in Banach and Frechet spaces
    Autorzy:
    Kasyanov, P. O.
    Mel'nik V., S.
    Piccirillo, A. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255055.pdf
    Data publikacji:
    2008
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    local subdifferential
    multi-variational inequality
    Frechet space
    Opis:
    Some functional-topological concepts of subdifferential and locally subdifferential maps in Frechet spaces are established. Multivariational inequalities with an operator of the pseudomonotone type, connected with subdifferential maps, are considered.
    Źródło:
    Opuscula Mathematica; 2008, 28, 3; 295-311
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Solution of a Finite Element Approximation of a Linear Obstacle Plate Problem
    Autorzy:
    Fernandes, L. M.
    Figueiredo, I. N.
    Judice, J. J.
    Powiązania:
    https://bibliotekanauki.pl/articles/907894.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    matematyka
    variational inequality
    complementarity problem
    contact problem
    Opis:
    In this paper the solution of a finite element approximation of a linear obstacle plate problem is investigated. A simple version of an interior point method and a block pivoting algorithm have been proposed for the solution of this problem. Special purpose implementations of these procedures are included and have been used in the solution of a set of test problems. The results of these experiences indicate that these procedures are quite efficient to deal with these instances and compare favourably with the path-following PATH and the active-set MINOS codes of the commercial GAMS collection
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2002, 12, 1; 27-40
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of a frictionless contact problem for elastic bodies
    Autorzy:
    Drabla, S.
    Sofonea, M.
    Teniou, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/1294377.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    frictionless contact
    elastic body
    variational inequality
    monotone operator
    penalized problem
    Opis:
    This paper deals with a nonlinear problem modelling the contact between an elastic body and a rigid foundation. The elastic constitutive law is assumed to be nonlinear and the contact is modelled by the well-known Signorini conditions. Two weak formulations of the model are presented and existence and uniqueness results are established using classical arguments of elliptic variational inequalities. Some equivalence results are presented and a strong convergence result involving a penalized problem is also proved.
    Źródło:
    Annales Polonici Mathematici; 1998, 69, 1; 75-88
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Robinsons implicit function theorem
    Autorzy:
    Dontchev, A. L.
    Powiązania:
    https://bibliotekanauki.pl/articles/970518.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    funkcja uwikłana
    czułość
    nierówność wariacyjna
    optymalizacja
    implicit function
    sensitivity
    variational inequality
    optimization
    Opis:
    Robinson's implicit function theorem has played a mayor role in the analysis of stability of optimization problems in the last two decades. In this paper we take a new look at this theorem, and with an updated terminology go back to the roots and present some extensions.
    Źródło:
    Control and Cybernetics; 2003, 32, 3; 529-541
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some results for the reflection problems in Hilbert spaces
    Autorzy:
    Barbu, V.
    Da Prato, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/970292.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    stochastic variational inequality
    Wiener processes in Hilbert spaces
    convex sets
    strong solutions
    Opis:
    This work is concerned with existence and uniqueness of a solution of a stochastic variational inequality on closed convex bounded subsets with nonempty interior and smooth boundary of a Hilbert space H (the reflection problem).
    Źródło:
    Control and Cybernetics; 2008, 37, 4; 797-810
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A new iterative method for generalized equilibrium and constrained convex minimization problems
    Autorzy:
    Yazdi, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/2078968.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Generalized equilibrium problem
    constrained convex minimization
    averaged mapping
    iterative method
    variational inequality
    Opis:
    The gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. In this paper, we combine the GPA and averaged mapping approach to propose an explicit composite iterative scheme for finding a common solution of a generalized equilibrium problem and a constrained convex minimization problem. Then, we prove a strong convergence theorem which improves and extends some recent results.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2020, 74, 2; 81-99
    0365-1029
    2083-7402
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On discontinuous quasi-variational inequalities
    Autorzy:
    Chu, Liang-Ju
    Lin, Ching-Yang
    Powiązania:
    https://bibliotekanauki.pl/articles/729419.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    variational inequality
    quasi-variatioal inequality
    Ricceri's conjecture
    Karamardian condition
    Hausdorff continuous multifunction
    Kneser's minimax inequality
    Opis:
    In this paper, we derive a general theorem concerning the quasi-variational inequality problem: find x̅ ∈ C and y̅ ∈ T(x̅) such that x̅ ∈ S(x̅) and
    ⟨y̅,z-x̅⟩ ≥ 0, ∀ z ∈ S(x̅),
    where C,D are two closed convex subsets of a normed linear space X with dual X*, and $T:X → 2^{X*}$ and $S:C → 2^D$ are multifunctions. In fact, we extend the above to an existence result proposed by Ricceri [12] for the case where the multifunction T is required only to satisfy some general assumption without any continuity. Under a kind of Karmardian's condition, we give a partial affirmative answer to an unbounded quasi-variational inequality problem.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 199-212
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis and numerical approximation of an elastic frictional contact problem with normal compliance
    Autorzy:
    Han, Weimin
    Sofonea, Mircea
    Powiązania:
    https://bibliotekanauki.pl/articles/1338688.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    normal compliance
    finite element approximation
    Coulomb's law
    error estimates
    frictional contact
    variational inequality
    fixed point
    Opis:
    We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and fixed point theory. Moreover, we show the continuous dependence of the solution on the contact conditions. We also study the finite element approximations of the problem and derive error estimates. Finally, we introduce an iterative method to solve the resulting finite element system.
    Źródło:
    Applicationes Mathematicae; 1999, 26, 4; 415-435
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dynamic Contact Problems With Velocity Conditions
    Autorzy:
    Chau, O.
    Motreanu, V. V.
    Powiązania:
    https://bibliotekanauki.pl/articles/907895.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    lepkosprężystość
    viscoelastic
    elastic
    subdifferential boundary condition
    dynamic process
    nonlinear hyperbolic variational inequality
    maximal monotone operator
    weak solution
    Opis:
    We consider dynamic problems which describe frictional contact between a body and a foundation. The constitutive law is viscoelastic or elastic and the frictional contact is modelled by a general subdifferential condition on the velocity, including the normal damped responses. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of second-order evolution variational inequalities. We show that the solutions of the viscoelastic problems converge to the solution of the corresponding elastic problem as the viscosity tensor tends to zero and when the frictional potential function converges to the corresponding function in the elastic problem
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2002, 12, 1; 17-26
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Variational inequalities in noncompact nonconvex regions
    Autorzy:
    Lin, Ching-Yan
    Chu, Liang-Ju
    Powiązania:
    https://bibliotekanauki.pl/articles/729495.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Nikaidô's coincidence theorem
    variational inequality
    nearly convex
    V₀-Karamardian condition
    Saigal condition
    acyclic multifunction
    algebraic interior
    bounding points
    Opis:
    In this paper, a general existence theorem on the generalized variational inequality problem GVI(T,C,ϕ) is derived by using our new versions of Nikaidô's coincidence theorem, for the case where the region C is noncompact and nonconvex, but merely is a nearly convex set. Equipped with a kind of V₀-Karamardian condition, this general existence theorem contains some existing ones as special cases. Based on a Saigal condition, we also modify the main theorem to obtain another existence theorem on GVI(T,C,ϕ), which generalizes a result of Fang and Peterson.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2003, 23, 1; 5-19
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Construction of a common element for the set of solutions of fixed point problems and generalized equilibrium problems in Hilbert spaces
    Autorzy:
    Khan, Muhammad Aqeel Ahmad
    Powiązania:
    https://bibliotekanauki.pl/articles/744677.pdf
    Data publikacji:
    2016-12-01
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    fixed point
    strict pseudo-contraction
    equilibrium problem
    variational inequality problem
    inverse strongly monotone mapping
    shrinking projection method
    Opis:
    In this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of k-strict pseudocontractions and two finite families of generalized equilibrium problems in the setting of Hilbert spaces. Strong convergence results of the proposed iterative algorithm together with some applications to solve the variational inequality problems are established in such setting. Our results generalize and improve various existing results in the current literature.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2016, 15
    2300-133X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Variational Analysis of a Frictional Contact Problem for the Bingham Fluid
    Autorzy:
    Awbi, B.
    Selmani, L.
    Sofonea, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/908296.pdf
    Data publikacji:
    1999
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    płyn binghamowski
    prawo Coulomba
    nierówność wariacyjna
    rozwiązanie słabe
    Bingham fluid
    damped response
    Coulomb's friction law
    quasi-variational inequality
    weak solution
    Opis:
    We consider a mathematical model which describes the flow of a Bingham fluid with friction. We assume a stationary flow and we model the contact with damped response and a local version of Coulomb's law of friction.The problem leads to a quasi-variational inequality for the velocity field. We establish the existence of a weak solution and, under additional assumptions, its uniqueness. The proofs are based on a new result obtained in (Motreanu and Sofonea, 1999). We also establish the continuous dependence of the solution with respect to the contact conditions.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 1999, 9, 2; 371-385
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A level set method in shape and topology optimization for variational inequalities
    Autorzy:
    Fulmański, P.
    Laurain, A.
    Scheid, J. F.
    Sokołowski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/929713.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    optymalizacja kształtu
    pochodna topologiczna
    nierówność wariacyjna
    analiza asymptotyczna
    shape optimization
    topological derivative
    level set method
    variational inequality
    asymptotic analysis
    Opis:
    The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 3; 413-430
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Topological derivatives for semilinear elliptic equations
    Autorzy:
    Iguernane, M.
    Nazarov, S. A.
    Roche, J. R.
    Sokolowski, J.
    Szulc, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/907655.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    optymalizacja kształtu
    pochodna topologiczna
    nierówność wariacyjna
    analiza asymptotyczna
    shape optimization
    topological derivative
    level set method
    variational inequality
    asymptotic analysis
    Opis:
    The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L [...] norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2009, 19, 2; 191-205
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A sign preserving mixed finite element approximation for contact problems
    Autorzy:
    Hild, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/907565.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    nierówność wariacyjna
    zagadnienie kontaktowe
    metoda elementów skończonych
    variational inequality
    positive operator
    averaging operator
    contact problem
    Signorini problem
    mixed finite element method
    Opis:
    This paper is concerned with the frictionless unilateral contact problem (i.e., a Signorini problem with the elasticity operator). We consider a mixed finite element method in which the unknowns are the displacement field and the contact pressure. The particularity of the method is that it furnishes a normal displacement field and a contact pressure satisfying the sign conditions of the continuous problem. The a priori error analysis of the method is closely linked with the study of a specific positivity preserving operator of averaging type which differs from the one of Chen and Nochetto. We show that this method is convergent and satisfies the same a priori error estimates as the standard approach in which the approximated contact pressure satisfies only a weak sign condition. Finally we perform some computations to illustrate and compare the sign preserving method with the standard approach.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2011, 21, 3; 487-498
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Topological sensitivity analysis for a coupled nonlinear problem with an obstacle
    Autorzy:
    Abdelbari, M.
    Nachi, K.
    Sokolowski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/205653.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    topological derivative
    shape optimization
    SteklovPoincaroperator
    Signorini problem
    variational inequality
    Helmholtz equation
    coupled partial differential equations
    conical differential
    asymptotic expansions
    singular perturbations of geometrical Romains
    truncated domain
    Opis:
    The Topological Derivative has been recognized as a powerful tool in obtaining the optimal topology for several kinds of engineering problems. This derivative provides the sensitivity of the cost functional for a boundary value problem for nucleation of a small hole or a small inclusion at a given point of the domain of integration. In this paper, we present a topological asymptotic analysis with respect to the size of singular domain perturbation for a coupled nonlinear PDEs system with an obstacle on the boundary. The domain decomposition method, referring to the SteklovPoincar´epseudo-differential operator, is employed for the asymptotic study of boundary value problem with respect to the size of singular domain perturbation. The method is based on the observation that the known expansion of the energy functional in the ring coincides with the expansion of the Steklov-Poincar´e operator on the boundary of the truncated domain with respekt to the small parameter, which measures the size of perturbation. In this way, the singular perturbation of the domain is reduced to the regular perturbation of the Steklov-Poincar´e map ping for the ring. The topological derivative for a tracking type shape functional is evaluated so as to obtain the useful formula for application in the numerical methods of shape and topology optimization.
    Źródło:
    Control and Cybernetics; 2017, 46, 1; 5-25
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    New versions on Nikaidôs coincidence theorem
    Autorzy:
    Chu, Liang-Ju
    Lin, Ching-Yan
    Powiązania:
    https://bibliotekanauki.pl/articles/729530.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Vietoris map
    Nikaidô's coincidence theorem
    Fan-type element
    Górniewicz-type fixed point theorem
    coincidence
    variational inequality
    acyclic multifunction
    partition of unity
    local intersection property
    KKM mapping
    locally selectionable multifunction
    Opis:
    In 1959, Nikaidô established a remarkable coincidence theorem in a compact Hausdorff topological space, to generalize and to give a unified treatment to the results of Gale regarding the existence of economic equilibrium and the theorems in game problems. The main purpose of the present paper is to deduce several generalized key results based on this very powerful result, together with some KKM property. Indeed, we shall simplify and reformulate a few coincidence theorems on acyclic multifunctions, as well as some Górniewicz-type fixed point theorems. Beyond the realm of monotonicity nor metrizability, the results derived here generalize and unify various earlier ones from the classic optimization theory. In the sequel, we shall deduce two versions of Nikaidô's coincidence theorem about Vietoris maps from different approaches.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2002, 22, 1; 79-95
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Pseudomonotone semicoercive variational-hemivariational inequalities with unilateral growth condition
    Autorzy:
    Naniewicz, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/206224.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    nierówność wariacyjno-hemiwariacyjna
    jednostronne warunki wzrostu
    variational-hemivariational inequality
    unilateral growth condition
    discontinuous subgradient
    Opis:
    A variational-hemivariational inequality on a vector valued function space is studied with the nonlinear part satisfying the unilateral growth condition. The higher order term is assumed to be pseudo-monotone and semicoercive. The compatibility condition expressed in terms of a recession functional has been proposed and the existence result has been formulated in a form involving the notion of discontinuous subgradient.
    Źródło:
    Control and Cybernetics; 2003, 32, 2; 223-244
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Discontinuous quasilinear elliptic problems at resonance
    Autorzy:
    Kourogenis, Nikolaos
    Papageorgiou, Nikolaos
    Powiązania:
    https://bibliotekanauki.pl/articles/966108.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    compact embedding
    Poincaré's inequality
    Palais-Smale condition
    critical point
    variational method
    Mountain Pass Theorem
    subdifferential
    problems at resonance
    locally Lipschitz functional
    Opis:
    In this paper we study a quasilinear resonant problem with discontinuous right hand side. To develop an existence theory we pass to a multivalued version of the problem, by filling in the gaps at the discontinuity points. We prove the existence of a nontrivial solution using a variational approach based on the critical point theory of nonsmooth locally Lipschitz functionals.
    Źródło:
    Colloquium Mathematicum; 1998, 78, 2; 213-223
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-24 z 24

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