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

Abstract

In this study, we investigate a nonlinear eigenvalue problem on a bounded domain in R^d, d ≥ 2. The existence of a nondecreasing sequence of nonnegative eigenvalues is established using the Ljusternik-Schnirelmann principle. Using the variational principle, we also prove that there exists a principal eigenvalue which is the smallest of all possible eigenvalues and that the set of eigenvalues is not closed.