Compact embeddings in the generalized Sobolev space W01,p(.)(G) and existence of solutions for nonlinear elliptic problems

被引：10

作者：

Ohno, Takao ^{[1
]}

机构：

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

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 5-6期

关键词：

Sobolev spaces of variable exponents; Compact embeddings; Nonlinear elliptic problems; LEBESGUE;

D O I：

10.1016/j.na.2008.12.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our aim in this Paper is to deal with the compact embedding in the generalized Sobolev space W-0(1,p(.))(G) with a variable exponent satisfying the log-Holder condition. As an application. we rind a nontrivial weak solution of the nonlinear elliptic problem -div(vertical bar del u(x)vertical bar(p(x)-2)del u(x)) = f(x, u(x)) in G, u(x) = 0 on partial derivative G, which is an extension of Fan-Zhang [X. Fan, G.-H. Zhang, Existence of solutions for p(x)-Laplacian Dirichlet problem, Nonlinear Anal. 52, 2003, pp. 1843-1852, Theorem 4.7]. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：1534 / 1541

页数：8