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Limit cycles for a class of fifth-order differential equations
Achref Eddine Tabet,Makhlouf Amar 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.1
The purpose of this research is to investigate sufficient conditions for the existence of limit cycles of the fifth-order differential equation \begin{equation*} x^{(5)}+(p^2+q^2)\overset{...}{x}+p^2q^2\overset{.}{x}=\varepsilon F(t,x,\overset{.}{x},\overset{..}{x},\overset{...}{x},\overset{....}{x}), \end{equation*} where $p,\;q$ are rational numbers different from $0$, $p\neq\pm q$, $\varepsilon$ is a small real parameter, and $F$ is a $2k\pi$-periodic function in the variable $t$. Also, we provide some applications.