Nonlinear Eigenvalue Problems for (p, 2)-Equations and Laplace Equations with Perturbations

Abstract

We consider two types of nonlinear eigenvalue problems involving Laplace and p-Laplace operators \((p>2)\). The main result establishes the existence of at least two nontrivial weak solutions in the case of the perturbed equation and the existence of a continuous spectrum in the case of the (p, 2)-equation. In both cases, variational methods play a central role in our arguments.