Periodic Solutions of a Class of Duffing Differential Equations (Journal of Nonlinear Modeling and Analysis, 2024)
In this work we study the existence of new periodic solutions for the well known class of Duffing differential equation of the form $x^{′′}+ c x^{′}+ a(t) x +b(t) x^3 = h(t)$, 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.
Keywords: Periodic solution; averaging method; Duffing differential equation; bifurcation; stability.