Periodic solutions for higher order differential equations with deviating argument

By using the coincidence degree theory of Mawhin, we study the existence of periodic solutions for higher order differential equations with deviating argument x(n)(t) = n−1 i=1 bix(i)(t)+f (t,x(t),x(t −τ1(t)), . . . , x(t −τm(t)))+p(t). Some new results on the existence of periodic solutions of the equations are obtained. Meanwhile, an example is given to illustrate our results. © 2008 Elsevier Inc. All rights reserved