Degenerate elliptic boundary value problems with asymptotically linear nonlinearity

The purpose of this paper is to study a class of semilinear degenerate elliptic boundary value problems with asymptotically linear nonlinearity which include as particular cases the Dirichlet and Robin problems. Our approach is based on the global inversion theorems between Banach spaces, and is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the theory of partial differential equations. By making use of the variational method, we prove existence and uniqueness theorems for our problem. The results here extend three earlier theorems due to Ambrosetti and Prodi to the degenerate case