On the existence of periodic solutions for the third-order nonlinear ordinary differential equations

In this paper, the existence of periodic solution for the third-order nonlinear ordinary differential equation of the form { } is considered, where f, g, h and p are the continuous functions, and p(t+T)=p(t). By using the Leray-Schauder degree method, some sufficient conditions to guarantee the existence of T periodic solution for the e-quation are obtained. Some previous results are extended and improved.