Nonlinear elliptic equations with a jumping reaction

Abstract

We study a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian and a Laplacian (2<p<+∞) and a jumping nonlinearity. Under very general conditions on the reaction and without using the Fučik spectrum, we show that the problem has at least three nontrivial solutions and we provide sign information for all of them. Our approach uses critical point theory, truncation and comparison techniques and Morse theory.