Nonlinear neumann problems near resonance

Abstract

We study nonlinear parametric Neumann problems driven by the p-Laplacian differential operator. We examine the existence and multiplicity of solutions and of positive solutions, when the parameter is near resonance. We consider two distinct cases. The first when the near resonance occurs from the left and the other when it occurs from the right. Our method of proof combines variational methods based on the critical point theory with Morse theoretic techniques. Indiana University Mathematics Journal ©.