Periodic solutions of sublinear Liénard differential equations

In this paper, we study the existence of periodic solutions of the second order differential equations x + f (x)x + g(x) = e(t). Using continuation lemma, we obtain the existence of periodic solutions provided that F(x) (= x 0 f (s)ds) is sublinear when x tends to positive infinity and g(x) satisfies a new condition xg (x) g(x) −M, x d, where M, d are two positive constants. © 2006 Elsevier Inc. All rights reserved.