Topological methods in the study of periodic solutions of non-smooth differential equations

Abstract

The main objective of this project consists in the study of limit cycles of continuous differential equations by means of topological tools such as the Brouwer degree and the coincidence degree. The theme of this project is strongly based on recent publications which generalize, for non-smooth differential equations, some classical techniques (Averaging Theory and Melnikov's Method) used in the study of the persistence of periodic solutions for, until latelly, sufficiently smooth differential equations. Such publications represent a considerable advance in the theory of bifurcation of limit cycles. In this project we will study these works as well as the topological methods used thereof and also generalize the results aforementioned for non-Lipschitzian systems. (AU)