On the nonlinear Neumann problem involving the critical Sobolev exponent and Hardy potential.

Abstract

In this paper we investigate the solvability of the Neumann problems (1), (12), (16), (32) and (43) involving the critical Sobolev and Hardy exponents. It is assumed that the coefficient Q is a positive and smooth function on ¯, µ and _ are real parameters. We examine the common effect of the mean curvature of the boundary @, the shape of the graph of the coefficient Q and the singular Hardy potential on the existence and the nonexistence of solutions of these problems.