On a Non-smooth Eigenvalue Problem in Orlicz-Sobolev Spaces

Abstract

This article studies a non-smooth eigenvalue problem for a Dirichlet boundary value inclusion on a bounded domain Ω which involves a -Laplacian and the generalized gradient in the sense of Clarke of a locally Lipschitz function depending also on the points in Ω. Specifically, the existence of a sequence of eigensolutions satisfying in addition certain asymptotic and locational properties is established. The approach relies on an approximation process in a suitable Orlicz–Sobolev space by eigenvalue problems in finite-dimensional spaces for which one can apply a finite-dimensional, non-smooth version of the Ljusternik–Schnirelman theorem. As a byproduct of our analysis, a version of Aubin–Clarke's theorem in Orlicz spaces is obtained.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Non-smooth eigenvalue problem; Orlicz-Sobolev spaces; finite dimensional approximation; Ljusternik-Schnirelman theory; Krasnoselskii genus

International Standard Serial Number (ISSN)

0003-6811

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2010 Taylor & Francis, All rights reserved.

Publication Date

01 Jan 2010

Link to Full Text

Share

 
COinS