On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent

被引：228

作者：

Mihailescu, Mihai ^{[1
]}

Radulescu, Vicentiu ^{[1
]}

机构：

[1] Univ Craiova, Dept Math, Craiova 200585, Romania

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2007年 / 135卷 / 09期

关键词：

D O I：

10.1090/S0002-9939-07-08815-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the nonlinear eigenvalue problem - div (vertical bar del u|(p(x)-2)del u) = lambda|u|(q(x)-2) u in Omega, u = 0 on partial derivative Omega, where Omega is a bounded open set in R-N with smooth boundary and p, q are continuous functions on (Omega) over bar such that 1 < inf(Omega) q < inf (Omega) p < sup(Omega) q, sup(Omega) p < N, and q(x) < Np(x)/(N-p(x)) for all x is an element of (Omega) over bar. The main result of this paper establishes that any lambda > 0 sufficiently small is an eigenvalue of the above nonhomogeneous quasilinear problem. The proof relies on simple variational arguments based on Ekeland's variational principle.

引用

页码：2929 / 2937

页数：9

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