Periodic solutions for a class of perturbed fifth-order autonomous differential equations via averaging theory

	Periodic solutions for a class of perturbed fifth-order autonomous differential equations via averaging theory
International Journal of Nonlinear Analysis and Applications
مقاله 200، دوره 13، شماره 2، مهر 2022، صفحه 2479-2491 اصل مقاله (404.8 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.26448.3317
نویسندگان
Chems Eddine Chems Eddine Berrehail^* ؛ Amar Makhlouf
Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, Annaba, 23000, Algeria
چکیده
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.
کلیدواژه‌ها
Periodic orbit؛ Fifth-order differential equation؛ Averaging theory
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