Eigenvalue problems for the p-Laplacian

We study nonlinear eigenvalue problems for the p-Laplace operator subject to different kinds of boundary conditions on a bounded domain. Using the Ljusternik-Schnirelman principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues. We prove the simplicity and isolation of the principal eigenvalue and give a characterization for the second eigenvalue. (c) 2005 Elsevier Ltd. All rights reserved.