On the Existence of Periodic Solutions for the Quasi-Linear Third-Order Differential Equation

AbstractIn this paper we consider the nonlinear third-order quasi-linear differential equationx‴+k2x′=ϵfx,x′,x″and obtain some simple conditions for the existence of a periodic solution for it. In so doing we use the implicit function theorem to prove a theorem about the existence of periodic solutions and consider one example to show the realizability of the conditions. The validity of the conditions for the parameter-free problemx‴+k2x′=fx,x′,x″also is considered