Eigenvalue problem for the weighted $p$-Laplacian

Abstract

In this paper we are concerned with the nonlinear eigenvalue problem for
the weighted $p$-Laplacian. The main result of the work is the existence of the
eigenpair for the Dirichlet problem provided that the weights are bounded.
Furthermore, under this assumption the eigenvector belongs to the Sobolev
space $W^{1p}_0 (\Omega)$.