Critical Neumann Problem with Competing Hardy Potentials

Abstract

In this paper we investigate the solvability of the nonlinear Neumann problem involving a critical Sobolev nonlinearity and two competing Hardy potentials in a bounded domain. We examine the common effect of the shape of the graph of the weight function, the mean curvature of the boundary and Hardy potentials on the existence of solutions of this problem. We are mainly interested in the existence of positive solutions. We also obtain the existence of sign-changing solutions.