On the critical Neumann problem with lower order perturbations

In this paper we investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent and lower order perturbations in bounded domains. Solutions are obtained by min max methods based on a topological linking. A nonlinear perturbations of a lower order is allowed to interfere with the spectrum of the Laplace operator with the Neumann boundary conditions.