A Quasilinear Eigenvalue Problem with Robin Conditions on the Non-Smooth Domain of Finite Measure

Abstract

In this paper, we consider a nonlinear eigenvalue problem involving the p-Laplacian with Robin boundary conditions on a domain of finite measure. We show the existence, simplicity and isolation of principal eigenvalue and regularity results for the corresponding eigenfunction. Furthermore we establish the link between the Dirichlet and Neumann problems by means of the Robin boundary conditions with variable parameter.