Existence of n positive solutions to a nonlinear second-order periodic boundary value problem

Key words:  nonlinear ordinary differential equation  periodic boundary value problem  positive solution  existence  multiplicity

Abstract:

By choosing suitable control functions and applying fixed point theorems on cone, the existence and multiplicity of positive solutions were studied for a class of nonlinear second-order periodic boundary value problems. The boundary value problem was transformed into an integral equation by Green's function of corresponding linear problem. Then the fixed points of the integral equation on cone were considered. The results show that the problem has at least n positive solutions provided the growth rates of nonlinear term are appropriate on certain bounded subsets of its domain, where n is an arbitrary positive integral number.