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    Wyświetlanie 1-46 z 46
    Tytuł:
    Existence results for Dirichlet problems with degenerated p-Laplacian
    Autorzy:
    Cavalheiro, A. C
    Powiązania:
    https://bibliotekanauki.pl/articles/254803.pdf
    Data publikacji:
    2013
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    degenerate elliptic equations
    entropy solutions
    weighted Sobolev spaces
    Opis:
    In this article, we prove the existence of entropy solutions for the Dirichlet problem [formula] where Ω is a bounded open set of [formula].
    Źródło:
    Opuscula Mathematica; 2013, 33, 3; 439-453
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hemivariational inequalities governed by the p-Laplacian -Dirichlet problem
    Autorzy:
    Naniewicz, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/970356.pdf
    Data publikacji:
    2004
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    zagadnienie Dirichleta
    nierówność hemiwariacyjna
    jednostronny warunek wzrostu
    teoria punktu krytycznego
    Dirichlet problem
    hemivariational inequality
    unilateral growth condition
    critical point theory
    locally Lipschitz functional
    Opis:
    A hemivariational inequality involving p-Laplacian is studied under the hypothesis that the nonlinear part fulfills the unilateral growth condition (Naniewicz, 1994). The existence of solutions for problems with Dirichlet boundary conditions is established by making use of Chang's version of the critical point theory for non-smooth locally Lipschitz functionals (Chang, 1981), combined with the Galerkin method. A class of problems with nonlinear potentials fulfilling the classical growth hypothesis without Ainbrosetti-Rabinowitz type assumption is discussed. The approach is based on the recession technique introduced in Naniewicz (2003).
    Źródło:
    Control and Cybernetics; 2004, 33, 2; 181-210
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hemivariational inequalities governed by the p-Laplacian - Neumann problem
    Autorzy:
    Naniewicz, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/970247.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Neumann problem
    noncoercive hemivariational inequality
    unilateral growth condition
    critical point theory
    locally Lipschitz functional
    Opis:
    A hemivariational inequality involving p-Laplacian is studied under the hypothesis that the nonlinear part fulfills the unilateral growth condition. The existence of solutions for problems with Neumann boundary conditions is established by making use of Chang's version of the critical point theory for nonsmooth locally Lipschitz functionals, combined with the Galerkin method. The approach is based on the recession technique introduced previously by the author.
    Źródło:
    Control and Cybernetics; 2007, 36, 3; 727-754
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the solvability of Dirichlet problem for the weighted p-Laplacian
    Autorzy:
    Szlachtowska, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/255957.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    p-Laplacian
    weak solutions
    solvability
    Opis:
    The paper investigates the existence and uniqueness of weak solutions for a non-linear boundary value problem involving the weighted ρ-Laplacian. Our approach is based on variational principles and representation properties of the associated spaces.
    Źródło:
    Opuscula Mathematica; 2012, 32, 4; 775-781
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Periodic solutions for second-order Hamiltonian systems with a p-Laplacian
    Autorzy:
    Zhang, Xingyong
    Tang, Xianhua
    Powiązania:
    https://bibliotekanauki.pl/articles/747033.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Second-order Hamiltonian systems
    p-Laplacian
    periodic solution
    Sobolev’s inequality
    Wirtinger’s inequality
    the least action principle
    Opis:
    In this paper, by using the least action principle, Sobolev’s inequality and Wirtinger’s inequality, some existence theorems are obtained for periodic solutions of second-order Hamiltonian systems with a p-Laplacian under subconvex condition, sublinear growth condition and linear growth condition. Our results generalize and improve those in the literature.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2010, 54, 1
    0365-1029
    2083-7402
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the solvability of Dirichlet problem for the weighted p-Laplacian
    Autorzy:
    Mielczarek, Dominik
    Rydlewski, Jerzy
    Szlachtowska, Ewa
    Powiązania:
    https://bibliotekanauki.pl/articles/729562.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    weighted p-Laplacian
    weak solutions
    solvability
    semi-inner product spaces
    Opis:
    In this paper we are concerned with the existence and uniqueness of the weak solution for the weighted p-Laplacian. The purpose of this paper is to discuss in some depth the problem of solvability of Dirichlet problem, therefore all proofs are contained in some detail. The main result of the work is the existence and uniqueness of the weak solution for the Dirichlet problem provided that the weights are bounded. Furthermore, under this assumption the solution belongs to the Sobolev space $W₀^{1,p}(Ω)$.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 1; 89-103
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some remarks on the optimization of eigenvalue problems involving the p-Laplacian
    Autorzy:
    Pielichowski, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/255346.pdf
    Data publikacji:
    2008
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    p-Laplacian
    first eigenvalue
    Steiner symmetry
    Opis:
    Given a bounded domain Ω ⊂ Rn, numbers p > 1, ∝ ≥ 0 and A ∈ /0, /Ω/], consider the optimization problem: find a subset D ⊂ Ω, of measure A, for which the first eigenvalue of the operator u → - div(/∇u/p-2 ∇u) + ∝ΧD/u/p-2u with the Dirichlet boundary condition is as small as possible. We show that the optimal configuration D is connected with the corresponding positive eigenfunction u in such a way that there exists a number t ≥ 0 for which D = { u ≤ t}. We also give a new proof of symmetry of optimal solutions in the case when Ω is Steiner symmetric and p = 2.
    Źródło:
    Opuscula Mathematica; 2008, 28, 4; 561-566
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions
    Autorzy:
    Hai, D. D.
    Wang, X.
    Powiązania:
    https://bibliotekanauki.pl/articles/255386.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    p-Laplacian
    semipositone
    nonlinear boundary conditions positive solutions
    Opis:
    We prove the existence of positive solutions for the p-Laplacian problem [formula] where [formula] can be nonlinear, i=1,2 , f:(0,∞)→R is p-superlinear or p-sublinear at ∞ and is allowed be singular (±∞) at 0, and λ is a positive parameter.
    Źródło:
    Opuscula Mathematica; 2019, 39, 5; 675-689
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A generalized periodic boundary value problem for the one-dimensional p-Laplacian
    Autorzy:
    Jiang, Daqing
    Wang, Junyu
    Powiązania:
    https://bibliotekanauki.pl/articles/1310724.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    generalized periodic boundary value problem
    p-Laplacian
    upper and lower solutions
    Carathéodory function
    Nagumo condition
    Opis:
    The generalized periodic boundary value problem -[g(u')]' = f(t,u,u'), a < t < b, with u(a) = ξu(b) + c and u'(b) = ηu'(a) is studied by using the generalized method of upper and lower solutions, where ξ,η ≥ 0, a, b, c are given real numbers, $g(s) = |s|^{p-2} s$, p > 1, and f is a Carathéodory function satisfying a Nagumo condition. The problem has a solution if and only if there exists a lower solution α and an upper solution β with α(t) ≤ β(t) for a ≤ t ≤ b.
    Źródło:
    Annales Polonici Mathematici; 1996-1997, 65, 3; 265-270
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and Multiplicity of Solutions for Noncoercive Neumann Problems with $p$-Laplacian
    Autorzy:
    Gasiński, Leszek
    Papageorgiou, Nikolaos S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1373561.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
    Tematy:
    Palais–Smale condition
    noncoercive functional
    second deformation theorem
    Opis:
    We consider a nonlinear Neumann elliptic equation driven by the $p$-Laplacian and a Carathéodory perturbation. The energy functional of the problem need not be coercive. Using variational methods we prove an existence theorem and a multiplicity theorem, producing two nontrivial smooth solutions. Our formulation incorporates strongly resonant equations..
    Źródło:
    Schedae Informaticae; 2012, 21; 27-40
    0860-0295
    2083-8476
    Pojawia się w:
    Schedae Informaticae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the existence of nonnegative radial solutions for p-Laplacian elliptic systems
    Autorzy:
    Jiang, Daqing
    Liu, Huizhao
    Powiązania:
    https://bibliotekanauki.pl/articles/1294162.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    elliptic system
    nonnegative radial solution
    existence
    fixed point theorem in cones
    Opis:
    The existence of nonnegative radial solutions for some systems of m (m ≥ 1) quasilinear elliptic equations is proved by a simple application of a fixed point theorem in cones.
    Źródło:
    Annales Polonici Mathematici; 1999, 71, 1; 19-29
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Uniqueness for a class p-Laplacian problems when a parameter is large
    Autorzy:
    Alreshidi, B.
    Hai, D. D.
    Powiązania:
    https://bibliotekanauki.pl/articles/29519620.pdf
    Data publikacji:
    2024
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    singular p-Laplacian
    uniqueness
    positive solutions
    Opis:
    We prove uniqueness of positive solutions for the problem $ −Δ_p u = \lambda f(u) $ in $ \Omega, u = 0 $ on $ \delta \Omega $, where $ 1 < p < 2 $ and $ p $ is close to 2, $ \Omega $ is bounded domain in $ \mathbb{R}^n $ with smooth boundary $ ∂Ω, f : [0,∞) → [0,∞) $ with $ f(z) ∼ z \beta $ at $ \infty $ for some $ \beta ∈ (0, 1) $, and $ \lambda $ is a large parameter. The monotonicity assumption on $ f $ is not required even for $ u $ large.
    Źródło:
    Opuscula Mathematica; 2024, 44, 1; 5-17
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the existence of five nontrivial solutions for resonant problems with p-Laplacian
    Autorzy:
    Gasiński, Leszek
    Papageorgiou, Nikolaos
    Powiązania:
    https://bibliotekanauki.pl/articles/729275.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    p-Laplacian
    Clarke subdifferential
    linking sets
    upper-lower solutions
    second eigenvalue
    nodal and constant sign solutions
    second deformation theorem
    Opis:
    In this paper we study a nonlinear Dirichlet elliptic differential equation driven by the p-Laplacian and with a nonsmooth potential. The hypotheses on the nonsmooth potential allow resonance with respect to the principal eigenvalue λ₁ > 0 of $(-Δₚ,W₀^{1,p}(Z))$. We prove the existence of five nontrivial smooth solutions, two positive, two negative and the fifth nodal.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 2; 169-189
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Constant-sign solutions for a nonlinear Neumann problem involving the discrete p-Laplacian
    Autorzy:
    Candito, P.
    D'Agui, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/255253.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    constant-sign solution
    difference equations
    Neumann problem
    Opis:
    In this paper, we investigate the existence of constant-sign solutions for a nonlinear Neumann boundary value problem involving the discrete p-Laplacian. Our approach is based on an abstract local minimum theorem and truncation techniques.
    Źródło:
    Opuscula Mathematica; 2014, 34, 4; 683-690
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonlinear elliptic equations involving the p-laplacian with mixed Dirichlet-Neumann boundary conditions
    Autorzy:
    Bonanno, Gabriele
    D'Agui, Giuseppina
    Sciammetta, Angela
    Powiązania:
    https://bibliotekanauki.pl/articles/254739.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    mixed problem
    critical points
    Opis:
    In this paper, a nonlinear differential problem involving the p-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results.
    Źródło:
    Opuscula Mathematica; 2019, 39, 2; 159-174
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Notes on aplications of the dual fountain theorem to local and nonlocal elliptic equations with variable exponent
    Autorzy:
    Stegliński, Robert
    Powiązania:
    https://bibliotekanauki.pl/articles/2216155.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    dual fountain theorem
    p(·)-Laplacian
    fractional p(·)-Laplacian
    infinitely many solution
    Opis:
    Using the Dual Fountain Theorem we obtain some existence of infinitely many solutions for local and nonlocal elliptic equations with variable exponent. Our results correct some of the errors that have appeared recently in the literature.
    Źródło:
    Opuscula Mathematica; 2022, 42, 5; 751-761
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The first eigencurve for a Neumann boundary problem involving p-Laplacian with essentially bounded weights
    Autorzy:
    Sanhaji, Ahmed
    Dakkak, Ahmed
    Moussaoui, Mimoun
    Powiązania:
    https://bibliotekanauki.pl/articles/29519370.pdf
    Data publikacji:
    2023
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    p-Laplacian
    first eigencurve
    singular weights
    Neumann boundary conditions
    Opis:
    This article is intended to prove the existence and uniqueness of the first eigencurve, for a homogeneous Neumann problem with singular weights associated with the equation $ −\Delta_p u = \alpha m_1 |u|^{p−2} u + \beta m_2 |u|^{p−2} u $ in a bounded domain $ \Omega \subset \mathbb{R}^N $. We then establish many properties of this eigencurve, particularly the continuity, variational characterization, asymptotic behavior, concavity and the differentiability.
    Źródło:
    Opuscula Mathematica; 2023, 43, 4; 559-574
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On existence of shape optimization for a p-Laplacian equation over a class of open domains
    Autorzy:
    Guo, Bao-Zhu.
    Yang, D. H.
    Powiązania:
    https://bibliotekanauki.pl/articles/206462.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Laplacian
    shape optimization
    existence
    Opis:
    In this paper, we introduce four new classes of open sets in general Euclidean space RN. It is shown that every such class of open sets is compact under the Hausdorff distance. The result is applied to a shape optimization problem of p-Laplacian equation. The existence of the optimal solution is presented.
    Źródło:
    Control and Cybernetics; 2014, 43, 1; 15-31
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Eigenvalue problems with indefinite weight
    Autorzy:
    Szulkin, Andrzej
    Willem, Michel
    Powiązania:
    https://bibliotekanauki.pl/articles/1217214.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    eigenvalue problem
    Laplacian
    p-Laplacian
    indefinite weight
    Opis:
    We consider the linear eigenvalue problem -Δu = λV(x)u, $u ∈ D^{1,2}_0(Ω)$, and its nonlinear generalization $-Δ_{p}u = λV(x)|u|^{p-2}u$, $u ∈ D^{1,p}_0(Ω)$. The set Ω need not be bounded, in particular, $Ω = ℝ^N$ is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues $λ_n → ∞$.
    Źródło:
    Studia Mathematica; 1999, 135, 2; 191-201
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian
    Autorzy:
    Liu, Bing
    Yu, Jianshe
    Powiązania:
    https://bibliotekanauki.pl/articles/1207894.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    a priori bounds
    boundary value problems
    existence theorems
    differential equations with deviating arguments
    Leray-Schauder degree
    p-Laplacian
    Opis:
    We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: $-(ϕ_{p}(x'))' + d/dt grad F(x) + g(t,x(t),x(δ(t))$, x'(t), x'(τ(t))) = 0, t ∈ [0,1]; $x(t)=\underline{φ}(t),$ t ≤ 0; $x(t) = \overline{φ}(t)$, t ≥ 1. An existence result is obtained with the help of the Leray-Schauder degree theory, with no restriction on the damping forces d/dt grad F(x).
    Źródło:
    Annales Polonici Mathematici; 2000, 75, 3; 271-280
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Properties of solutions to some weighted ρLlaplacian equation
    Autorzy:
    Garain, Prashanta
    Powiązania:
    https://bibliotekanauki.pl/articles/952844.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    p-Laplacian
    degenerate elliptic equations
    weighted Sobolev space
    Opis:
    In this paper, we prove some qualitative properties for the positive solutions to some degenerate elliptic equation given by [formula] on smooth domain and for varying nonlinearity ∫.
    Źródło:
    Opuscula Mathematica; 2020, 40, 4; 483-494
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of positive radial solutions to a p-Laplacian Kirchhoff type problem on the exterior of a ball
    Autorzy:
    Graef, John R.
    Hebboul, Doudja
    Moussaoui, Toufik
    Powiązania:
    https://bibliotekanauki.pl/articles/29519226.pdf
    Data publikacji:
    2023
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Kirchhoff problem
    p-Laplacian
    positive radial solution
    variational methods
    Opis:
    In this paper the authors study the existence of positive radial solutions to the Kirchhoff type problem involving the p-Laplacian $ -(a+b \sum_{\Omega_e} | \nabla u |^p dx) \Delta_p u = \lambda f (|x|, u), x ∈ \Omega_e, u=0 $ on $ \delta \Omega_e $, where λ > 0 is a parameter, $ Ω_e = {x ∈ \mathbb{R}^N : |x| > r_0}, r_0 > 0, N > p > 1, Δp $ is the p-Laplacian operator, and $ f ∈ C([r_0,+∞) × [0,+∞) , \mathbb{R} ) $ is a non-decreasing function with respect to its second variable. By using the Mountain Pass Theorem, they prove the existence of positive radial solutions for small values of λ.
    Źródło:
    Opuscula Mathematica; 2023, 43, 1; 47-66
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities
    Autorzy:
    Papageorgiou, Nikolaos
    Papalini, Francesca
    Powiązania:
    https://bibliotekanauki.pl/articles/1207915.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    eigenvalues
    multivalued problem
    discontinuous term
    p-Laplacian
    subdifferential
    locally Lipschitz functional
    Opis:
    We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.
    Źródło:
    Annales Polonici Mathematici; 2000, 75, 2; 125-141
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence Result for Differential Inclusion with $p(x)$-Laplacian
    Autorzy:
    Barnaś, Sylwia
    Powiązania:
    https://bibliotekanauki.pl/articles/1373553.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
    Tematy:
    Palais–Smale condition
    mountain pass theorem
    variable exponent Sobolev space
    $p(x)$-Laplacian
    Opis:
    In this paper we study the nonlinear elliptic problem with $p(x)$-Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to ChangIn this paper we study the nonlinear elliptic problem with $p(x)$-Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to Chang
    Źródło:
    Schedae Informaticae; 2012, 21; 41-54
    0860-0295
    2083-8476
    Pojawia się w:
    Schedae Informaticae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence result for hemivariational inequality involving p(x)-Laplacian
    Autorzy:
    Barnaś, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/254855.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    p(x)-Laplacian
    Palais-Smale condition
    mountain pass theorem
    variable exponent Sobolev space
    Opis:
    In this paper we study the nonlinear elliptic problem with p(x)-Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to Chang [J. Math. Anal. Appl. 80 (1981), 102-129].
    Źródło:
    Opuscula Mathematica; 2012, 32, 3; 439-454
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Three Solutions Theorem for a Quasilinear Dirichlet Boundary Value Problem
    Autorzy:
    Goncerz, Paweł
    Powiązania:
    https://bibliotekanauki.pl/articles/1373559.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
    Tematy:
    Carathéodory funtion
    Dirihlet problem
    three ritial points theorem
    weak solution
    $p$-Laplacian
    Opis:
    We consider a Dirichlet boundary value problem driven by the $p$-Laplacian with the right hand side being a Carathéodory function. The existence of solutions is obtained by the use of a special form of the three critical points theorem.
    Źródło:
    Schedae Informaticae; 2012, 21; 159-168
    0860-0295
    2083-8476
    Pojawia się w:
    Schedae Informaticae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Energy decay result for a nonlinear wave p-Laplace equation with a delay term
    Autorzy:
    Laouar, Lakhdar Kassah
    Khaled, Zennir
    Powiązania:
    https://bibliotekanauki.pl/articles/748364.pdf
    Data publikacji:
    2017
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Nonlinear wave equation, Time varying delay term, Decay rate, Multiplier method, p-Laplacian.
    Opis:
    We consider the nonlinear (in space and time) wave equation with delay term in the internal feedback. Under conditions on the delay term and the term without delay, we study the asymptotic behavior of solutions using the multiplier method and general weighted integral inequalities.
    Źródło:
    Mathematica Applicanda; 2017, 45, 1
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional p&q-Laplacian problems with potentials vanishing at infinity
    Autorzy:
    Isernia, Teresa
    Powiązania:
    https://bibliotekanauki.pl/articles/254783.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fractional p&g-Laplacian
    vanishing potentials
    ground state solution
    Opis:
    In this paper we prove the existence of a positive and a negative ground state weak solution for the following class of fractional p&g-Laplacian problems [formula] where [formula]and [formula] are continuous, positive functions, allowed for vanishing behavior at infinity, ƒ is a continuous function with quasicritical growth and the leading operator [formula] , with t ∈ {p, q}, is the fractional t-Laplacian operator.
    Źródło:
    Opuscula Mathematica; 2020, 40, 1; 93-110
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the existence of three solutions for quasilinear elliptic problem
    Autorzy:
    Goncerz, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/254869.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    critical point
    elliptic problem
    minimax inequality
    p-Laplacian
    three critical points theorem
    weak solution
    Opis:
    We consider a quasilinear elliptic problem of the type - Δpu = λ (ƒ (u)+ μg(u)) in Ω, u/∂Ω = 0, where Ω ⊂ RN is an open and bounded set, ƒ, g are continuous real functions on R and , λ, μ ∈ R. We prove the existence of at least three solutions for this problem using the so called three critical points theorem due to Ricceri.
    Źródło:
    Opuscula Mathematica; 2012, 32, 3; 473-486
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian
    Autorzy:
    Barnaś, Sylwia
    Powiązania:
    https://bibliotekanauki.pl/articles/729528.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    p(x)-Laplacian
    hemivariational inequality
    Cerami condition
    mountain pass theorem
    variable exponent Sobolev space
    Opis:
    In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang [6] and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 1; 15-39
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Steklov problem involving the p(x)-laplacian with indefinite weight
    Autorzy:
    Ali, B. K.
    Ghanmi, A.
    Kefi, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/255266.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    p(x)-Laplace operator
    Steklov problem
    variable exponent Sobolev spaces
    variational methods
    Ekeland's variational principle
    Opis:
    Under suitable assumptions, we study the existence of a weak nontrivial solution for the following Steklov problem involving the p(x)-Laplacian [formula] Our approach is based on min-max method and Ekeland's variational principle.
    Źródło:
    Opuscula Mathematica; 2017, 37, 6; 779-794
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Continuous spectrum of Steklov nonhomogeneous elliptic problem
    Autorzy:
    Allaoui, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/254696.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Steklov problem
    critical point theorem
    p(x)-Laplacian
    Opis:
    By applying two versions of the mountain pass theorem and Ekeland's variational principle, we prove three different situations of the existence of solutions for the following Steklov problem: [formula] where Ω ⊂ RN (N ≥ 2) is a bounded smooth domain and p, q: Ω → (1, + ∞) are continuous functions.
    Źródło:
    Opuscula Mathematica; 2015, 35, 6; 853-866
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solutions for a nonhomogeneous p&q-Laplacian problem via variational methods and sub-supersolution technique
    Autorzy:
    Tavares, Leandro S.
    Sousa, J. Vanterler C.
    Powiązania:
    https://bibliotekanauki.pl/articles/29519368.pdf
    Data publikacji:
    2023
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    p&q-Laplacian operator
    nonhomogeneous operator
    sub-supersolution
    existence
    multiplicity
    Opis:
    In this paper it is obtained, through variational methods and sub-supersolution arguments, existence and multiplicity of solutions for a nonhomogeneous problem which arise in several branches of science such as chemical reactions, biophysics and plasma physics. Under a general hypothesis it is proved an existence result and multiple solutions are obtained by considering an additional natural condition.
    Źródło:
    Opuscula Mathematica; 2023, 43, 4; 603-613
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and multiplicity results for nonlinear problems involving the p(x)-laplace operator
    Autorzy:
    Tsouli, N.
    Darhouche, O.
    Powiązania:
    https://bibliotekanauki.pl/articles/256023.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    critical points
    variational method
    generalized Lebesgue-Sobolev spaces
    p(x)-Laplacian
    Opis:
    In this paper we study the following nonlinear boundary-value problem [formula] where Ω ⊂ RN is a bounded domain with smooth boundary [formula] is the outer unit normal derivative on [formula] are two real numbers such that [formula] is a continuous function on Ω with [formula] are continuous functions. Under appropriate assumptions on ƒ and g, we obtain the existence and multiplicity of solutions using the variational method. The positive solution of the problem is also considered.
    Źródło:
    Opuscula Mathematica; 2014, 34, 3; 621-638
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multiple solutions for nonlinear discontinuous elliptic problems near resonance
    Autorzy:
    Kourogenis, Nikolaos
    Papageorgiou, Nikolaos
    Powiązania:
    https://bibliotekanauki.pl/articles/965892.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    discontinuous function
    generalized directional derivative
    critical point
    coercive functional
    multiple solutions
    Clarke subdifferential
    Rayleigh quotient
    first eigenvalue
    p-Laplacian
    elliptic inclusion
    nonsmooth Palais-Smale condition
    Opis:
    We consider a quasilinear elliptic eigenvalue problem with a discontinuous right hand side. To be able to have an existence theory, we pass to a multivalued problem (elliptic inclusion). Using a variational approach based on the critical point theory for locally Lipschitz functions, we show that we have at least three nontrivial solutions when $λ → λ_1$ from the left, $λ_1$ being the principal eigenvalue of the p-Laplacian with the Dirichlet boundary conditions.
    Źródło:
    Colloquium Mathematicum; 1999, 81, 1; 89-99
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An integro-differential inequality related to the smallest positive eigenvalue of<i>p</i>(<i>x</i>)-Laplacian Dirichlet problem
    Autorzy:
    Wiśniewski, Damian
    Bodzioch, Mariusz
    Powiązania:
    https://bibliotekanauki.pl/articles/744689.pdf
    Data publikacji:
    2016-12-01
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    p(x)-Laplacian
    eigenvalue
    variable exponent Sobolev space
    Dirichlet problem
    unbounded domain
    Opis:
    We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.
    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:
    Singular quasilinear convective systems involving variable exponents
    Autorzy:
    Moussaoui, Abdelkrim
    Nabab, Dany
    Vélin, Jean
    Powiązania:
    https://bibliotekanauki.pl/articles/29519640.pdf
    Data publikacji:
    2024
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    p(x)-Laplacian
    variable exponents
    fixed point
    singular system
    gradient estimates
    regularity
    Opis:
    The paper deals with the existence of solutions for quasilinear elliptic systems involving singular and convection terms with variable exponents. The approach combines the sub-supersolutions method and Schauder’s fixed point theorem.
    Źródło:
    Opuscula Mathematica; 2024, 44, 1; 105-134
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the dependence on parameters for second order discrete boundary value problems with the p(k)-Laplacian
    Autorzy:
    Smejda, J.
    Wieteska, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/952772.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    discrete boundary value problems
    variational methods
    mountain pass theorem
    Opis:
    In this paper we study the existence and the nonexistence of solutions for the boundary value problems of a class of nonlinear second-order discrete equations depending on a parameter. Variational (the mountain pass technique) and non-variational methods are applied.
    Źródło:
    Opuscula Mathematica; 2014, 34, 4; 851-870
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On optimal and quasi-optimal controls in coefficients for multi-dimensional thermistor problem with mixed Dirichlet-Neumann boundary conditions
    Autorzy:
    Kogut, Peter I.
    Powiązania:
    https://bibliotekanauki.pl/articles/970117.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    nonlinear elliptic equations
    control in coefficients
    p(x)-Laplacian
    approximation approach
    thermistor problem
    Opis:
    In this paper we deal with an optimal control problem in coefficients for the system of two coupled elliptic equations, also known as the thermistor problem, which provides a simultaneous description of the electric field u = u(x) and temperature θ(x). The coefficients of the operator div (B(x)∇θ(x)) are used as the controls in L∞(Ω). The optimal control problem is to minimize the discrepancy between a given distribution θd ∈ Lr(Ω) and the temperature of thermistor θ ∈ W1,γ 0 (Ω) by choosing an appropriate anisotropic heat conductivity matrix B. Basing on the perturbation theory of extremal problems and the concept of fictitious controls, we propose an “approximation approach” and discuss the existence of the so-called quasi-optimal and optimal solutions to the given problem.
    Źródło:
    Control and Cybernetics; 2019, 48, 1; 31-68
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multiplicity results for an impulsive boundary value problem of p(t)-Kirchhoff type via critical point theory
    Autorzy:
    Mokhtari, A.
    Moussaoui, T.
    O'Regan, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/255007.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    genus theory
    nonlocal problems
    impulsive conditions
    Kirchhoff equation
    p(i)-Laplacian
    variational methods
    critical point theory
    Opis:
    In this paper we obtain existence results of k distinct pairs nontrivial solutions for an impulsive boundary value problem of p(t)-Kirchhoff type under certain conditions on the parameter λ.
    Źródło:
    Opuscula Mathematica; 2016, 36, 5; 631-649
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Neumann boundary value problem for a class of gradient systems
    Autorzy:
    Pan, W. W.
    Li, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/255138.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Neumann problems
    weak solutions
    critical points
    (p1, . . . , pn)-Laplacian
    Opis:
    In this paper we study a class of two-point boundary value systems. Using very recent critical points theorems, we establish the existence of one non-trivial solution and infinitely many solutions of this problem, respectively.
    Źródło:
    Opuscula Mathematica; 2014, 34, 1; 171-181
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Laplacian mesh smoothing for tetrahedra based volume visualization
    Autorzy:
    Stęgierski, R.
    Mikołajczak, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/333809.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Śląski. Wydział Informatyki i Nauki o Materiałach. Instytut Informatyki. Zakład Systemów Komputerowych
    Tematy:
    dane seryjne
    generacja trójkąta sieci
    wyrównywanie sieci
    maszerujące czworościany
    volume data
    triangle mesh generation
    mesh smoothing
    marching tetrahedra
    Opis:
    In this paper an improved method for three-dimensional (3-D) surface reconstruction from computed tomography slices is presented. Marching cubes (MC) is a popular method for extracting iso-surfaces from discrete (3-D) data. We implemented a simplification of marching cubes, commonly known as marching tetrahedrons (MT).
    Źródło:
    Journal of Medical Informatics & Technologies; 2002, 4; MT11-18
    1642-6037
    Pojawia się w:
    Journal of Medical Informatics & Technologies
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Crystal Density Prediction, Charge Density Distribution and the Explosive Properties of the Highly Energetic Molecule 2-Methyl-5-nitramino-tetrazole: a DFT and AIM Study
    Autorzy:
    Srinivasan, P.
    Kumaradhas, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/358115.pdf
    Data publikacji:
    2013
    Wydawca:
    Sieć Badawcza Łukasiewicz - Instytut Przemysłu Organicznego
    Tematy:
    crystal density
    electron density
    Laplacian of electron density
    impact sensitivity
    electrostatic potential
    Opis:
    The ab initio crystal density, bond topological and explosive properties of the energetic molecule 2-methyl-5-nitraminotetrazole (MNAT) have been calculated by the MOLPAK/PMIN software and the AIM theory. The density predicted from the crystal structure simulation almost matches the experimental density. The geometrical parameters of the molecule lifted from the crystal structure are in very close agreement with the reported X-ray molecular structure. The bond topological analysis predicts a signifcantly low bond electron density, as well as a less Laplacian of electron density, for the N–NO2 bond. The Laplacian for the bond to the attached methyl group, the C(2)–N(2) bond, is also found to be less negative; the less negative values of the Laplacian confrms that these are the weakest bonds in the molecule. The impact sensitivity (h50) of the molecule has been calculated, and is almost equal to the reported experimental value. The sensitivity of the molecule was also estimated from the electrostatic imbalance parameter and has the value ν = 0.242. The isosurface of the electrostatic potential of the molecule displays a high negative electrostatic potential region around the tetrazole ring and the nitramine N–N bond, which are the possible reactive locations in the molecule.
    Źródło:
    Central European Journal of Energetic Materials; 2013, 10, 1; 53-68
    1733-7178
    Pojawia się w:
    Central European Journal of Energetic Materials
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Charge Density Distribution, Electrostatic Properties and Sensitivity of the Highly Energetic Molecule 2,4,6-Trinitro-1,3,5-triazine: A Theoretical Study
    Autorzy:
    Srinivasan, P.
    Maheshwari, K.
    Jothi, M.
    Kumaradhas, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/358320.pdf
    Data publikacji:
    2012
    Wydawca:
    Sieć Badawcza Łukasiewicz - Instytut Przemysłu Organicznego
    Tematy:
    energetic molecule
    electron density
    Laplacian of electron density
    electrostatic potential
    impact sensitivity
    Opis:
    Ab initio and density functional theory (DFT) calculations were carried out on the energetic propellant molecule 2,4,6-trinitro-1,3,5-triazine (TNTA) to understand its bond topology and its energetic properties using the theory of atoms in molecules (AIM). The DFT method predicts that the electron density ρ bcp (r) at the bond critical points of ring C-N bonds is ∼ 2.34 e Å -3 and the corresponding Laplacian ∇ 2 ρ bcp(r) is ∼ -24.4 e Å -5 ; whereas these values are found to be very small in the -NO2 group attached to C-N bonds [ρ bcp(r): ∼ 1.73 e Å -3 and Δ 2 ρ bcp (r): ∼ -14.5 e Å -5 ]. The negative Laplacian values of C-NO 2 bonds are significantly lower which indicates that the charges of these bonds are highly depleted. The C-NO2 bonds exhibit low bond order (∼ 0.8), as well as low (∼ 56.4 kcal/mol) bond dissociation energy. As we reported in our earlier studies, we found high bond charge depletion for these bonds, which are considered the weakest bonds in the molecule. The frontier orbital energies exhibit a wide band gap, which is larger than those of existing molecules TATB, TNT and TNB. The impact sensitivity (H 50 %) (4.2 m) and oxygen balance (2.77%) were calculated and compared with related structures. Large negative electrostatic potential regions were found near the nitro groups where reaction is expected to occur. The relation between charge depletion ∇ 2 ρ bcp(r) and the electrostatic potential at the bond midpoints V mid reveals the sensitive areas of the molecule.
    Źródło:
    Central European Journal of Energetic Materials; 2012, 9, 1; 59-76
    1733-7178
    Pojawia się w:
    Central European Journal of Energetic Materials
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Frames and factorization of graph Laplacians
    Autorzy:
    Jorgensen, P.
    Tian, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/255936.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    unbounded operators
    deficiency-indices
    Hilbert space
    boundary values
    weighted graph
    reproducing kernel
    Dirichlet form
    graph Laplacian
    resistance network
    harmonic analysis
    frame
    Parseval frame
    Friedrichs extension
    reversible random walk
    resistance distance
    energy Hilbert space
    Opis:
    Using functions from electrical networks (graphs with resistors assigned to edges), we prove existence (with explicit formulas) of a canonical Parseval frame in the energy Hilbert space [formula] of a prescribed infinite (or finite) network. Outside degenerate cases, our Parseval frame is not an orthonormal basis. We apply our frame to prove a number of explicit results: With our Parseval frame and related closable operators in [formula] we characterize the Priedrichs extension of the [formula]-graph Laplacian. We consider infinite connected network-graphs G = (V, E), V for vertices, and E for edges. To every conductance function c on the edges E of G, there is an associated pair [formula] where [formula] in an energy Hilbert space, and Δ (=Δc) is the c-graph Laplacian; both depending on the choice of conductance function c. When a conductance function is given, there is a current-induced orientation on the set of edges and an associated natural Parseval frame in [formula] consisting of dipoles. Now Δ is a well-defined semibounded Hermitian operator in both of the Hilbert [formula] and [formula]. It is known to automatically be essentially selfadjoint as an [formula]-operator, but generally not as an [formula] operator. Hence as an [formula] operator it has a Friedrichs extension. In this paper we offer two results for the Priedrichs extension: a characterization and a factorization. The latter is via [formula].
    Źródło:
    Opuscula Mathematica; 2015, 35, 3; 293-332
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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