Existence and multiplicity of solutions for resonant nonlinear Neumann problems

Abstract

We consider nonlinear Neumann problems driven by the pLaplacian differential operator with a Caratheodory nonlinearity. Under hypotheses which allow resonance with respect to the principal eigenvalue λ0 = 0 at ±∞, we prove existence and multiplicity results. Our approach is variational and uses critical point theory and Morse theory (critical groups).