Sufficient conditions for the existence of periodic solutions to some second order differential equations with a deviating argument ✩

By means of Mawhin’s continuation theorem, we study some second order differential equations with a deviating argument: x (t) = f t,x(t),x t −τ(t) , x (t) +e(t). Some new results on the existence of periodic solutions are obtained. The interest is that we allow the degree with respect to the variables x0, x1, x2 of f (t,x0, x1, x2) to be greater than 1; and also the result (Theorem 3.2) is related to the deviating argument τ(t). Meanwhile, we give an example to demonstrate our result.  2004 Elsevier Inc. All rights reserved.