Global positive solution branches of positone problems with nonlinear boundary conditions

Abstract

In this paper we consider a class of semilinear elliptic boundary value problems with nonlinear boundary conditions. The continuation method or the implicit function theorem is used to prove the existence of smooth branches of positive solutions. The characterization of the branches, and the uniqueness and asymptotic behavior of positive solutions are also studied by using some comparison principles with semilinear elliptic boundary value problems with linear boundary conditions.