Existence of positive solutions of second-order delayed differential
system on infinite interval

- Ran Ding,
- Fanglei Wang,
- Nannan Yang,
- Yuanfang RU

## Abstract

The present paper is focused on the analysis on the existence of positive solutions of a second order differential system with two delays

\begin{equation}
\left\{\begin{array}{lcr}x_{1}^{\prime\prime}(t)-a_{1}(t)x_{1}(t)+m_{1}(t)f_{1}(t,x(t),x_{\tau}(t))=0,\ \ t>0,\\
x_{2}^{\prime\prime}(t)-a_{2}(t)x_{2}(t)+m_{2}(t)f_{2}(t,x(t),x_{\tau}(t))=0,\ \ t>0,\\
x_{1}(t)=0,\ \ -\tau_{1}\ \leq t\leq 0,\;\text{and}\;\lim_{t\rightarrow\infty}x_{1}(t)=0,\\
x_{2}(t)=0,\ \ -\tau_{2}\ \leq t\leq 0,\;\text{and}\;\lim_{t\rightarrow\infty}x_{2}(t)=0\end{array}\right.\nonumber \\
\end{equation}
by using two well-known fixed point theorems.

23 Feb 2020Submitted to *Mathematical Methods in the Applied Sciences* 28 Feb 2020Assigned to Editor

28 Feb 2020Submission Checks Completed

10 Jul 2020Reviewer(s) Assigned