Anti-periodic solutions of Liénard equations with state dependent impulses

Abstract

Subject to a priori bounds, Liénard equations with state dependent impulsive forcing are shown to admit a unique absolutely continuous anti-periodic solution with first derivative of bounded variation on finite intervals. The point-wise convergence of a sequence of iterates to the solution is obtained, along with a bound for the rate of convergence. The results are applied to Josephson's and van der Pol's equations.