Volume 3, Issue 3-1, June 2015, Page: 54-59
Existence of Solutions to a Second Order Coupled System with Nonlinear Coupled Boundary Conditions
Naseer Ahmad Asif, Department of Mathematics, School of Science and Technology, University of Management and Technology, CII Johar Town, Lahore, Pakistan
Imran Talib, Department of Mathematics, School of Science and Technology, University of Management and Technology, CII Johar Town, Lahore, Pakistan
Received: Apr. 17, 2015;       Accepted: Apr. 20, 2015;       Published: Jun. 17, 2015
DOI: 10.11648/j.ajam.s.2015030301.19      View  3354      Downloads  93
Abstract
We study existence of solution in the presence of upper and lower solutions of some second-order nonlinear coupled ordinary differential system (ODS for short) depending on first order derivatives with nonlinear coupled boundary conditions (CBCs for short). Our method for nonlinear coupled system with nonlinear CBCs is new and it unifies the treatment of many different second order problems. Nagumo condition is used to define bound for the derivative of the solution. Coupled lower and upper solutions, Arzela-Ascoli theorem and Schauder's fixed point theorem play an important role in establishing the arguments.
Keywords
Lower and Upper Solutions, Coupled System, Coupled Boundary Conditions, Arzela-Ascoli Theorem, Schauder's Fixed Point Theorem
To cite this article
Naseer Ahmad Asif, Imran Talib, Existence of Solutions to a Second Order Coupled System with Nonlinear Coupled Boundary Conditions, American Journal of Applied Mathematics. Special Issue:Proceedings of the 1st UMT National Conference on Pure and Applied Mathematics (1st UNCPAM 2015). Vol. 3, No. 3-1, 2015, pp. 54-59. doi: 10.11648/j.ajam.s.2015030301.19
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