Existence of solutions for p(x)-Laplacian Dirichlet problem

被引：787

作者：

Fan, XL ^{[1
]}

Zhang, QH ^{[1
]}

机构：

[1] Lanzhou Univ, Dept Math, Lanzhou 730000, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2003年 / 52卷 / 08期

关键词：

p(x)-laplacian; integral functionals; generalized Lebesgue-Sobolev spaces; critical points;

D O I：

10.1016/S0362-546X(02)00150-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents several sufficient conditions for the existence of solutions for the Dirichlet problem of p(x)-Laplacian {-div(\delu\ (p(x)-2)delu) = f(x,u), x is an element of Omega, {u = 0, xis an element of partial derivativeOmega. Especially, an existence criterion for infinite many pairs of solutions for the problem is obtained. The discussion is based on the theory of the spaces L-p(x) (Omega) and W-0(1, p(x)) (Omega). (C) 2003 Elsevier Science Ltd. All rights reserved.

引用

页码：1843 / 1852

页数：10

共 50 条

[1] Existence of radial solutions for a p(x)-Laplacian Dirichlet problem
Ragusa, Maria Alessandra
Razani, Abdolrahman
Safari, Farzaneh
ADVANCES IN DIFFERENCE EQUATIONS, 2021, 2021 (01):
[2] On the existence and stability of solutions for Dirichlet problem with p(x)-Laplacian
Galewski, Marek
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 326 (01) : 352 - 362
[3] Existence of solutions for a Dirichlet problem with a p-Laplacian
Yuan, Jian-Jun
Ou, Zeng-Qi
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 397 (02) : 577 - 585
[4] Existence of Solution for Dirichlet Problem with p(x)-Laplacian
Moussaoui, M.
Elbouyahyaoui, L.
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2015, 33 (02): : 241 - 248
[5] EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A DIRICHLET PROBLEM INVOLVING PERTURBED p(x)-LAPLACIAN OPERATOR
Abdou, Aboubacar
Marcos, Aboubacar
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2016,
[6] Existence and multiplicity of solutions for a Dirichlet problem involving the discrete p(x)-Laplacian operator
Mashiyev, Rabil
Yucedag, Zehra
Ogras, Sezgin
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2011, (67)
[7] Existence of non-zero solutions for a Dirichlet problem driven by (p(x),q(x)-Laplacian
Chinni, A.
Sciammetta, A.
Tornatore, E.
APPLICABLE ANALYSIS, 2022, 101 (15) : 5323 - 5333
[8] Existence of solutions for a nonhomogeneous Dirichlet problem involving p(x)-Laplacian operator and indefinite weight
Marcos, Aboubacar
Abdou, Aboubacar
BOUNDARY VALUE PROBLEMS, 2019, 2019 (01):
[9] EXISTENCE OF POSITIVE SOLUTIONS FOR A SINGULAR p-LAPLACIAN DIRICHLET PROBLEM
Zhou, Wenshu
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2008,
[10] On the Existence of Solutions of the Dirichlet Problem for the p-Laplacian on Riemannian Manifolds
Bakiev, S. M.
Kon'kov, A. A.
MATHEMATICAL NOTES, 2023, 114 (5-6) : 679 - 686

← 1 2 3 4 5 →