Periodic solutions of discontinuous second order differential systems

© 2014, Worldwide Center of Mathematics. All Rights reserved. We provide suffcient 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. Key words and phrases. periodic solution, autonomous discontinuous second order differential equations, non- autonomous discontinuous second order differential equations.