Existence and nonexistence of positive solutions for parametric Neumann problems with $p$-Laplacian

Abstract

Using variational methods based on the critical point theory and suitable truncation and comparison techniques, we study existence, multiplicity and nonexistence of positive solutions for a parametric nonlinear Neumann problem driven by the $p$-Laplacian. Our hypotheses cover the case of nonlinearities of concave-convex type whose exponents depend on the parameter.