loading page

Existence of positive solutions of second-order delayed differential system on infinite interval
  • +1
  • Ran Ding,
  • Fanglei Wang,
  • Nannan Yang,
  • Yuanfang RU
Ran Ding
Hohai University
Author Profile
Fanglei Wang
College of Science, Hohai University
Author Profile
Nannan Yang
Hohai University
Author Profile
Yuanfang RU
China Pharmaceutical University
Author Profile

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.

Peer review status:UNDER REVIEW

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