Existence and Multiplicity of Solutions for Neumann p-Laplacian-Type Equations

We consider nonlinear Neumann problems driven by p-Laplacian-type operators which are not homogeneous in general. We prove all existence and a multiplicity result for such problems. In the existence theorem, we assume that the right hand side nonlinearity is p-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. In the multiplicity result, when specialized to the case of the p-Laplacian, we allow strong resonance at; infinity and resonance at 0.