Periodic Solutions for a Class of n-th Order Functional Differential Equations

Abstract

We study the existence of periodic solutions for n-th order functional differential equations $x^{(n)}(t)={\displaystyle {\sum }_{i=0}^{n-1}{b}_i{[x^{(i)}(t)]}^k+f(x(t-\tau (t)))+p(t)}$. Some new results on the existence of periodic solutions of the equations are obtained. Our approach is based on the coincidence degree theory of Mawhin.