Existence and uniqueness theorems for semilinear elliptic boundary value problems

Abstract

This paper is devoted to the study of a class of degenerateboundary value problems for semilinear second-order elliptic differential operators depending nonlinearly on $\nabla u$. The purpose of this paper is to prove existence and uniqueness theorems of solutions of semilinear elliptic boundary value problems, by making use of the super-subsolution method and the Leray-Schauder degree theory. We remark that the variational method approach would fail, since our boundary condition is degenerate.