On the Eigenvalue problem involving the Robin p (x)-Lap1acian

Abstract

A nonlinear eigenvalue problem with Robin boundary conditions on a bounded domain is investigated. The existence of a sequence of non-negative eigenvalues is established using the Ljusternik-Shnirelmann principle. Using the variational principle, we also prove that there exists a principal eigenvalue which is the smallest of all the eigenvalues and that the set of eigenvalues is not closed.