Existence of periodic solution for perturbed generalized Lienard equations

Abstract

Under conditions of Levinson-Smith type, we prove the existence of a τ-periodic solution for the perturbed generalized Liénard equation u″ + φ(u, u′)u′ + ψ(u) = ɛω(t/τ, u, u′) with periodic forcing term. Also we deduce sufficient condition for existence of a periodic solution for the equation u″ + [u2 + (u + u′)2 - 1]u′ + u = ɛω(t/τ, u, u′). The results obtained are illustrated with numerical examples.