Positive solutions of nonlinear second-order periodic boundary value problems

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