Periodic Solutions of a Class of Duffing Differential Equations

Abstract

In this work we study the existence of new periodic solutions for the well known class of Duffing differential equation of the form $x^{\prime\prime}+ c x^{\prime}+ a(t) x +b(t) x^3 = h(t)$, where $c$ is a real parameter, $a(t)$, $b(t)$ and $h(t)$ are continuous $T$–periodic functions. Our results are proved using three different results on the averaging theory of first order.