On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Mihai Mihailescu Vicentiu Radulescu

Affiliation:	Department of Mathematics, University of Craiova, 200585 Craiova, Romania ; Department of Mathematics, University of Craiova, 200585 Craiova, Romania

Abstract:	We consider the nonlinear eigenvalue problem $displaystyle -{rm div}left(vertnabla uvert^{p(x)-2}nabla uright)=lambda vert uvert^{q(x)-2}u$ in , on , where is a bounded open set in $mathbb{R}^N$ with smooth boundary and , are continuous functions on such that , , and for all . The main result of this paper establishes that any sufficiently small is an eigenvalue of the above nonhomogeneous quasilinear problem. The proof relies on simple variational arguments based on Ekeland's variational principle.

Keywords:

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载全文