COMPACT EMBEDDINGS FOR SOBOLEV SPACES OF VARIABLE EXPONENTS AND EXISTENCE OF SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS INVOLVING THE p(x)-LAPLACIAN AND ITS CRITICAL EXPONENT

被引：0

作者：

Mizuta, Yoshihiro ^{[1
]}

Ohno, Takao ^{[2
]}

Shimomura, Tetsu ^{[3
]}

Shioji, Naoki ^{[4
]}

机构：

[1] Hiroshima Univ, Dept Math, Grad Sch Sci, Higashihiroshima 7398521, Japan

[2] Hiroshima Natl Coll Maritime Technol, Osakikamijima, Hiroshima 7250231, Japan

[3] Hiroshima Univ, Dept Math, Grad Sch Educ, Higashihiroshima 7398524, Japan

[4] Yokohama Natl Univ, Dept Math, Hodogaya Ku, Yokohama, Kanagawa 2408501, Japan

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2010年 / 35卷 / 01期

关键词：

Sobolev spaces of variable exponents; compact embeddings; nonlinear elliptic problems; GENERALIZED LEBESGUE; RIESZ-POTENTIALS; EQUATIONS; TOPOLOGY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a sufficient condition for the compact embedding from W-0(k,p(.))(Omega) to L-q(.)(Omega) in case ess in f(x epsilon Omega)(Np(x)/(N - kp(x)) - q(x)) = 0, where Omega is a bounded open set in R-N. As an application, we find a nontrivial nonnegative weak solution of the nonlinear elliptic equation -div (|del u(x)|(p(x)-2)del u(x)) = |u(x)|(q(x)-2)u(x) = in Omega, u(x) = 0 on partial derivative Omega. We also consider the existence of a weak solution to the problem above even if the embedding is not compact.

引用

页码：115 / 130

页数：16

共 50 条

[41] An existence result for a fractional elliptic system involving (p,q)-Laplacian and critical exponent
Zhang, Aini
Deng, Zhiying
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2023, 68 (05) : 746 - 762
[42] Multi-bump solutions for nonlinear elliptic equations involving critical Sobolev exponents
Jin, Sangdon
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 220
[43] Multiple solutions for inhomogeneous elliptic problems involving critical Sobolev-Hardy exponents
Kang, DS
Deng, YB
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 60 (04) : 729 - 753
[44] MULTIPLE SOLUTIONS FOR ELLIPTIC PROBLEMS INVOLVING THE p(x)-LAPLACIAN
Bonanno, Gabriele
Chinni, Antonia
MATEMATICHE, 2011, 66 (01): : 105 - 113
[45] Existence Results for Nonlinear Elliptic Equations with Leray–Lions Operators in Sobolev Spaces with Variable Exponents
M. Mosa Al-Shomrani
M. Ben Mohamed Salah
A. Ghanmi
K. Kefi
Mathematical Notes, 2021, 110 : 830 - 841
[46] Multiple positive solutions for indefinite semilinear elliptic problems involving a critical Sobolev exponent
Chen, Ching-yu
Wu, Tsung-fang
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2014, 144 (04) : 691 - 709
[47] POSITIVE SOLUTIONS OF PERTURBED ELLIPTIC PROBLEMS INVOLVING HARDY POTENTIAL AND CRITICAL SOBOLEV EXPONENT
Zhang, Jing
Ma, Shiwang
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2016, 21 (06): : 1999 - 2009
[48] Existence of solutions for several semi-linear elliptic equations involving critical sobolev exponents
Yang, Lin
Yang, Zhihuo
Chengdu Kejidaxue Xuebao/Journal of Chengdu University of Science and Technology, 1992, (04):
[49] EXISTENCE OF SOLUTIONS FOR ELLIPTIC SYSTEMS IN RN INVOLVING THE p(x)-LAPLACIAN
Djellit, Ali
Youbi, Zahra
Tas, Saadia
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2012,
[50] Existence of Solutions for Elliptic Systems Involving the Fractional p(x)-Laplacian
Lalili, Hadjira
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2024, 42

← 1 2 3 4 5 →