Nontrivial solutions for nonvariational quasilinear Neumann problems

Abstract

We consider a nonlinear nonvariational Neumann problem with a nonsmooth potential. Using the spectrum of the assymptotic (as $\vert x\vert \rightarrow\infty)$ differential operator and degree theoretic techniques based on the degree map of certain multivalued perturbations of (S)$_{+}$-operators, we establish the existence of at least one nontrivial smooth solution.