Many periodic solutions for a second order cubic periodic differential equation

Abstract

The aim of this work is to provide results that assure the existence of many isolated T-periodic solutions for T-periodic second-order differential equations of the form $$x''=a(t)x + b(t)x^2 + c(t)x^3$$ . We use bifurcation methods, including Malkin functions and results of Fonda, Sabatini and Zanolin. In addition, we give a general result that assures the existence of a T-periodic perturbation of a non-isochronous center with an arbitrary number of T-periodic solutions.