فهرست نشریات علمی دسترسی آزاد ایران

In this work, we use the averaging theory of first order to study the periodic solutions of the perturbed fifth-order autonomous differential equation\begin{equation*}x^{(5)}- \lambda \ddddot{x}+(p^{2}+1) \dddot{x}-\lambda(p^{2}+1)\ddot{x}+p^{2}\dot{x}-\lambda p^{2}x= \varepsilon F(x,\dot{x}, \ddot{x}, \dddot{x}, \ddddot{x}),\end{equation*}where $\lambda ,$ and $\varepsilon $ are real parameters, $p$ is rational number different from $-1,$ $0,$ $1$, $\varepsilon $ is a small enough and $F\in C^2 $ is a nonlinear autonomous function. we present some applications to illustrate our main results.