Existence and multiplicity of solutions for resonant nonlinear Neumann problems

Abstract

We consider nonlinear Neumann problems driven by the $p$-Laplacian differential operator with a Caratheodory nonlinearity. Under hypotheses which allow resonance with respect to the principal eigenvalue $\lambda_{0}$ $=0$ at $\pm\infty$, we prove existence and multiplicity results. Our approach is variational and uses critical point theory and Morse theory (critical groups).