On the periodic orbits of the fourth-order differential equation u⁗+qu″−u=εF(u,u′,u″,u‴)u⁗+qu″−u=εF(u,u′,u″,u‴)

We provide sufficient conditions for the existence of periodic solutions of the fourth-order differential equationu⁗+qu″−u=εF(u,u′,u″,u‴),u⁗+qu″−u=εF(u,u′,u″,u‴), where q and ε are real parameters, ε is small and F is a nonlinear function.