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 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.
V. K. Le et al., "On a Non-smooth Eigenvalue Problem in Orlicz-Sobolev Spaces," Applicable Analysis, Taylor & Francis, Jan 2010.
The definitive version is available at http://dx.doi.org/10.1080/00036810802428987
Mathematics and Statistics
Keywords and Phrases
Non-smooth eigenvalue problem; Orlicz-Sobolev spaces; finite dimensional approximation; Ljusternik-Schnirelman theory; Krasnoselskii genus
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