Infinitely many solutions for an elliptic Neumann problem involving critical Sobolev growth

In this paper, we prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth... This paper is arranged as follows. In Section 2, we will derive some integral estimates which are needed in the proof of Theorem 1.1. In Section 3, we will prove that the boundary blow-up cannot occur under the condition that all the principal curvatures of ∂Ω are nonnegative and the largest principal curvature is positive. The estimates in Section 3 are quite different from the problem with Dirichlet boundary condition studied in [10]. In Section 4, we prove that the interior blow-up cannot occur. In Appendices A and B, we give some existence results on the peak solutions, so as to justify the assumptions imposed in Theorem 1.1.