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)x″+f(x)x′+g(x)=e(t). Using continuation lemma, we obtain the existence of periodic solutions provided that F(x)F(x) (=∫0xf(s)ds) is sublinear when x   tends to positive infinity and g(x)g(x) satisfies a new conditionxg′(x)g(x)⩾−M,x⩾d, where M, d are two positive constants.