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.This is a preprint of: "Many periodic solutions for a second order cubic periodic differential equation",