For EDITORS

For READERS

All Issues

Vol.10, 2020
Vol.9, 2019
Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
Volume 10, Number 6, 2020, Pages 2659-2668                                                                DOI:10.11948/20200014
Positive periodic solutions for a nonlinear differential system with two parameters
Ruixiong Fan,Chengbo Zhai
Keywords:Positive periodic solutions, differential system, existence and uniqueness.
Abstract:
      In this article, we investigate a nonlinear system of differential equations with two parameters $$\left\{ \begin{array}{l} x""(t)=a(t)x(t)-\lambda f(t, x(t), y(t)),\y""(t)=-b(t)y(t)+\mu g(t, x(t), y(t)),\end{array}\right.$$ where $a,b \in C(\textbf{R},\textbf{R}_+)$ are $\omega-$periodic for some period $\omega > 0$, $a,b \not\equiv 0$, $f,g \in C(\textbf{R} \times \textbf{R}_+ \times \textbf{R}_+ ,\textbf{R}_+)$ are $\omega-$periodic functions in $t$, $\lambda$ and $\mu$ are positive parameters. Based upon a new fixed point theorem, we establish sufficient conditions for the existence and uniqueness of positive periodic solutions to this system for any fixed $\lambda,\mu>0$. Finally, we give a simple example to illustrate our main result.
PDF      Download reader