Periodic solutions of discontinuous second order differential systems

Journal of Singularities
volume 10 (2014), 183-190

Received 2 February 2013. Received in revised form 16 July 2013.

DOI: 10.5427/jsing.2014.10l

Add a reference to this article to your citeulike library.

Abstract:

We provide sufficient conditions for the existence of periodic solutions of some classes of autonomous and non-autonomous second order differential equations with discontinuous right-hand sides. In the plane the discontinuities considered are given by the straight lines either x=0, or xy=0. Two applications of these results are made, one to control systems with variable structure, and the other to small external periodic excitation of a discontinuous nonlinear oscillator.

Keywords:

periodic solution, autonomous discontinuous second order differential equations, non-autonomous discontinuous second order differential equations

Mathematical Subject Classification:

34C29, 34C25, 47H11

Author(s) information: