Multiplicity of positive solutions to semilinear elliptic boundary value problems

Abstract

We study semilinear elliptic boundary value problems of one parameter dependence where the number of positive solutions is discussed. Our main purpose is to characterize the critical value given by the infimum of such parameters for which positive solutions exist. Our approach is based on super- and sub-solutions, and relies on the topological degree theory on the positive cones of ordered Banach spaces. A concrete example is also presented.