Electron. J. Diff. Equ., Vol. 2015 (2015), No. 313, pp. 1-11.

Existence of solutions to second-order nonlinear coupled systems with nonlinear coupled boundary conditions

Imran Talib, Naseer Ahmad Asif, Cemil Tunc

Abstract:
In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations
$$\displaylines{ u''(t)=f(t,v(t)),\quad t\in [0,1],\cr v''(t)=g(t,u(t)),\quad t\in [0,1], }$$
with nonlinear coupled boundary conditions
$$\displaylines{ \phi(u(0),v(0),u(1),v(1),u'(0),v'(0))=(0,0), \cr \psi(u(0),v(0),u(1),v(1),u'(1),v'(1))=(0,0), }$$
where $f,g:[0,1]\times \mathbb{R}\to \mathbb{R}$ and $\phi,\psi:\mathbb{R}^6\to \mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.

Submitted July 14, 2015. Published December 24, 2015.
Math Subject Classifications: 34B10, 34B15.
Key Words: Lower and upper solutions; coupled system; coupled boundary conditions; Arzela-Ascoli theorem; Schauder's fixed point theorem.

Show me the PDF file (221 KB), TEX file, and other files for this article.

Imran Talib
Department of Mathematics, School of Science
University of Management and Technology
CII Johar Town, Lahore, Pakistan
email: imrantaalib@gmail.com
Naseer Ahmad Asif
Department of Mathematics, School of Science
University of Management and Technology
CII Johar Town, Lahore, Pakistan
email: naseerasif@yahoo.com
Cemil Tunc
Department of Mathematics Faculty of Sciences
Yuzuncu Yil University, Van - Turkey
email: cemtunc@yahoo.com

Return to the EJDE web page