On a non-smooth eigenvalue problem in Orlicz-Sobolev spaces

This article studies a non-smooth eigenvalue problem for a Dirichlet boundary value inclusion on a bounded domain which involves a phi-Laplacian and the generalized gradient in the sense of Clarke of a locally Lipschitz function depending also on the points in . 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.