Infinitely many periodic solutions of Duffing equations under integral condition

Abstract

In this paper, we study the multiplicity of periodic solutions of a Duffing equation $$ x''+g(x)=p(t). $$ By using the generalized Poincaré-Birkhoff fixed point theroem, we prove that this equation has infinitely many periodic solutions provided $g$ satisfies a kind of integral condition and the related time map satisfies oscillating condition.