Periodic solutions of a class of non-autonomous second order differential equations with discontinuous right-hand side

Author(s)

Jacquemard, A. ^[1] ; Teixeira, M. A. ^[2]

Affiliation

^[1] Univ Bourgogne, CNRS, IMB, UMR 5584, Dijon - France

^[2] Univ Estadual Campinas, Inst Matemat & Estat, Campinas, SP - Brazil

• Document type: Journal article
• Source: PHYSICA D-NONLINEAR PHENOMENA; v. 241, n. 22, p. 2003-2009, NOV 15 2012.
• Web of Science Citations: 19

Abstract

The main goal of this paper is to discuss the existence of periodic solutions of the second order equation: y `' + eta sgn(y) = alpha sin(beta t) with (eta, alpha, beta) is an element of R-3 eta > 0. We analyze the dynamics of such an equation around the origin which is a typical singularity of nonsmooth dynamical systems. The main results consist in exhibiting conditions on the existence of typical periodic solutions that appear generically in such systems. We emphasize that the mechanism employed here is applicable to many more systems. In fact this work fits into a general program for understanding the dynamics of non-autonomous differential equations with discontinuous right-hand sides. (C) 2011 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 07/06896-5 - Geometry of control, dynamical and stochastic systems
• Grantee: Luiz Antonio Barrera San Martin
• Support Opportunities: Research Projects - Thematic Grants