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

Naseer Ahmad Asif; Imran Talib

doi:doi:10.11648/j.ajam.s.2015030301.19

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

Naseer Ahmad Asif, Imran Talib

Published in American Journal of Applied Mathematics (Volume 3, Issue 3-1)

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

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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.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 3-1) This article belongs to the Special Issue Proceedings of the 1st UMT National Conference on Pure and Applied Mathematics (1st UNCPAM 2015)
DOI	10.11648/j.ajam.s.2015030301.19
Page(s)	54-59
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Lower and Upper Solutions, Coupled System, Coupled Boundary Conditions, Arzela-Ascoli Theorem, Schauder's Fixed Point Theorem

References

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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

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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

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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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@article{10.11648/j.ajam.s.2015030301.19,
  author = {Naseer Ahmad Asif and Imran Talib},
  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},
  url = {https://doi.org/10.11648/j.ajam.s.2015030301.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030301.19},
  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.},
 year = {2015}
}

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TY  - JOUR
T1  - Existence of Solutions to a Second Order Coupled System with Nonlinear Coupled Boundary Conditions
AU  - Naseer Ahmad Asif
AU  - Imran Talib
Y1  - 2015/06/17
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.s.2015030301.19
DO  - 10.11648/j.ajam.s.2015030301.19
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 54
EP  - 59
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.s.2015030301.19
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.
VL  - 3
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Author Information

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

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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

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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

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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

Copy | Download

@article{10.11648/j.ajam.s.2015030301.19,
  author = {Naseer Ahmad Asif and Imran Talib},
  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},
  url = {https://doi.org/10.11648/j.ajam.s.2015030301.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030301.19},
  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.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Existence of Solutions to a Second Order Coupled System with Nonlinear Coupled Boundary Conditions
AU  - Naseer Ahmad Asif
AU  - Imran Talib
Y1  - 2015/06/17
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.s.2015030301.19
DO  - 10.11648/j.ajam.s.2015030301.19
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 54
EP  - 59
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.s.2015030301.19
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.
VL  - 3
IS  - 3-1
ER  -

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