Periodic Solutions Of Impact Oscillator With Damping

Impact oscillator is an important model of dynamical system with discontinuity [8] .There are also relations with dual billiards[2], celestial mechanics [5]and Fermi accerator[9].Dynamics of impact oscillator is far from being understood, although some results are known [2, 3, 9, 10, 11, 12].In this paper,we study the periodic solutions of the impact oscillator with damping.First part,using continuation lemma and approximation method,we prove the existence of 2 -periodic admissible solutions for a class of second order bouncing differencial equations with damping.Second part,using approximation method and implicit function theorem,we obtain the existence of large amplitude 2 -periodic bouncing for damped linear impact osillator with mutiple impacts in one period.