### Existence of Solutions to a Second Order Coupled System with Nonlinear Coupled Boundary Conditions

Received: 17 April 2015    Accepted: 20 April 2015    Published: 17 June 2015

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

References
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• APA Style

Naseer Ahmad Asif, Imran Talib. (2015). Existence of Solutions to a Second Order Coupled System with Nonlinear Coupled Boundary Conditions. American Journal of Applied Mathematics, 3(3-1), 54-59. https://doi.org/10.11648/j.ajam.s.2015030301.19

ACS Style

Naseer Ahmad Asif; Imran Talib. Existence of Solutions to a Second Order Coupled System with Nonlinear Coupled Boundary Conditions. Am. J. Appl. Math. 2015, 3(3-1), 54-59. doi: 10.11648/j.ajam.s.2015030301.19

AMA Style

Naseer Ahmad Asif, Imran Talib. Existence of Solutions to a Second Order Coupled System with Nonlinear Coupled Boundary Conditions. Am J Appl Math. 2015;3(3-1):54-59. doi: 10.11648/j.ajam.s.2015030301.19

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title = {Existence of Solutions to a Second Order Coupled System with Nonlinear Coupled Boundary Conditions},
journal = {American Journal of Applied Mathematics},
volume = {3},
number = {3-1},
pages = {54-59},
doi = {10.11648/j.ajam.s.2015030301.19},
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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.},
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AB  - 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.
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Author Information
• Department of Mathematics, School of Science and Technology, University of Management and Technology, CII Johar Town, Lahore, Pakistan

• Department of Mathematics, School of Science and Technology, University of Management and Technology, CII Johar Town, Lahore, Pakistan

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