Two bounded solutions of opposite sign for nonlinear hemivariational inequalities at resonance

Abstract

In this paper we study quasilinear hemivariational inequalities at resonance at the first eigenvalue of the p-Laplacian. For such problems we establish the existence of at least two bounded solutions: one positive and the other negative. Our approach is based on the method of upper-lower solutions and on techniques from the theory of nonlinear operator of monotone type.