Periodic Solution of a Certain Non-Linear Third Order Differential Equation

In this paper, the third order differential equation x''''+\psi(x'')x''+(k^2+\phi(x))x''+f(t,x)=e(t) is considered. Under certain conditions on the functions appearing in the differential equation, the existence of periodic solutions is proved. Similar problems have been treated by authors in [4,6,7]. However, the method employed here is used by Reissig [1] and the results obtained are, in fact, a generalization of those in [1-3]. The conditions imposed on the nonlinear terms do not require the ultimate boundedness of all solutions.