Anti-Periodic Solutions for a Kind of High Order Differential Equations with Multi-Delay

Abstract

In this paper, using the Leray-Schauder degree theory, the new results on the existence and uniqueness of anti-periodic solutions are established for a kind of nonlinear high order differential equations with multiple deviating arguments of the form \begin{eqnarray*} x^{(n)}(t)+f(t,x^{(n-1)}(t))+\sum_{i=1}^n g_i(t,x(t-\tau_i(t)))=e(t) \end{eqnarray*} Finally, an example is also given to demonstrate the obtaining results.