Necessary and sufficient conditions for boundedness and oscillation in the retarded Liénard equation

Bo Zhang, Fayetteville State University

Abstract

Consider the retarded Liénard equation x? + f(x)x? + g(x(t - h)) = 0, where f, g: R ? R are continuous and h ? 0. Using Liapunov's direct method, we give necessary and sufficient conditions to ensure boundedness and oscillation of all solutions and their derivatives. © 1996 Academic Press, Inc.