Positive solutions of nonlinear second-order periodic boundary value problems

Abstract

In this paper, we consider the nonlinear second-order periodic boundary value problem u ″ ( t ) = f ( t , u ( t ) ) , a.e. t ∈ [ 0 , 2 π ] ; u ( 0 ) = u ( 2 π ) , u ′ ( 0 ) = u ′ ( 2 π ) , where the nonlinear term f is a Caratheodory function. By introducing two height functions concerned with f and considering the integrals of height functions on some bounded sets, we prove the existence and multiplicity of positive solutions for the problem.