American Journal of Applied Mathematics

| Peer-Reviewed |

Positive Solutions of a Singular System with Two Point Coupled Boundary Conditions

Received: 31 May 2015    Accepted: 01 June 2015    Published: 15 June 2015
Views:       Downloads:

Share This Article

Abstract

In this paper, we study the existence of positive solutions to a system of nonlinear differential equations subject to two-point coupled boundary conditions. Further, the nonlinearities are allowed to be singular with respect to first order derivatives. An example is included to show the applicability of our result.

DOI 10.11648/j.ajam.s.2015030301.14
Published in American Journal of Applied Mathematics (Volume 3, Issue 3-1, June 2015)

This article belongs to the Special Issue Proceedings of the 1st UMT National Conference on Pure and Applied Mathematics (1st UNCPAM 2015)

Page(s) 19-24
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), 2024. Published by Science Publishing Group

Keywords

Positive Solutions, Coupled System, Singular Ordinary Differential Equations, Coupled Boundary Conditions

References
[1] R. P. Agarwal and D. O’Regan, Singular Differential and Integral Equations with Applications, Kluwer Academic Publishers, Dordrecht, 2003.
[2] S. Agmon, A. Douglis, L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math. 17 (1964) 35-92.
[3] H. Amann, Parabolic evolution equations with nonlinear boundary conditions, in: Nonlinear Functional Analysis and Its Applications, Berkeley, 1983, in: Proc. Sympos. Pure Math., vol. 45, Amer. Math. Soc., Providence, RI, 1986, pp. 17-27.
[4] H. Amann, Parabolic evolution equations and nonlinear boundary conditions, J. Differential Equations 72 (1988) 201-269.
[5] D.G. Aronson, A comparison method for stability analysis of nonlinear parabolic problems, SIAM Rev 20 (1978), 245-264.
[6] N.A. Asif, P.W. Eloe and R.A. Khan, Positive solutions for a system of singular second order nonlocal boundary value problems, Jounnal of the Korean Mathematical Society, 47 (5) (2010) 985 - 1000.
[7] N.A. Asif and R.A. Khan, Positive solutions for a class of coupled system of singular three point boundary value problems, Boundary Value Problems 2009 (2009), Article ID 273063, 18 pages.
[8] N.A. Asif, R.A. Khan and J. Henderson, Existence of positive solutions to a system of singular boundary value problems, Dynamic Systems and Applications, 19 (2010) 395 – 404.
[9] X. Cheng and C. Zhong, Existence of positive solutions for a second-order ordinary differential system, J. Math. Anal. Appl. 312 (2005) 14–23.
[10] R.A. Khan and J.R.L. Webb, Existence of at least three solutions of nonlinear three point boundary value problems with super-quadratic growth, J. Math. Anal. Appl. 328 (2007) 690–698.
[11] A. Leung, A semilinear reactiondiffusion preypredator system with nonlinear coupled boundary conditions: Equilibrium and stability, Indiana Univ. Math. J. 31 (1982) 223-241.
[12] Y. Liu and B. Yan, Multiple solutions of singular boundary value problems for differential systems, J. Math. Anal. Appl. 287 (2003) 540–556.
[13] H. L¨u, H. Yu and Y. Liu, Positive solutions for singular boundary value problems of a coupled system of differential equations, J. Math. Anal. Appl. 302 (2005), 14–29.
[14] F. Ali Mehmeti, Nonlinear Waves in Networks, Math. Res., vol. 80, Akademie-Verlag, Berlin, 1994.
[15] F. Ali Mehmeti, S. Nicaise, Nonlinear interaction problems, Nonlinear Anal. 20 (1993) 27-61.
[16] S. Nicaise, Polygonal Interface Problems, Methoden und Verfahren der Mathematischen Physik, vol. 39, Peter Lang, Frankfurt Main, 1993.
[17] Z. Wei, Positive solution of singular Dirichlet boundary value problems for second order differential equation system, J. Math. Anal. Appl. 328 (2007) 1255–1267.
[18] X. Xian, Existence and multiplicity of positive solutions for multi-parameter three-point differential equations system, J. Math. Anal. Appl. 324 (2006) 472–490.
[19] A. Zettl, Sturm-Liouvillie Theory, Math. Surveys Monogr., vol. 121, Amer. Math. Soc., Providence, RI, 2005.
Author Information
  • Department of Mathematics, School of Science and Technology, University of Management and Technology, Lahore, Pakistan

Cite This Article
  • APA Style

    Naseer Ahmad Asif. (2015). Positive Solutions of a Singular System with Two Point Coupled Boundary Conditions. American Journal of Applied Mathematics, 3(3-1), 19-24. https://doi.org/10.11648/j.ajam.s.2015030301.14

    Copy | Download

    ACS Style

    Naseer Ahmad Asif. Positive Solutions of a Singular System with Two Point Coupled Boundary Conditions. Am. J. Appl. Math. 2015, 3(3-1), 19-24. doi: 10.11648/j.ajam.s.2015030301.14

    Copy | Download

    AMA Style

    Naseer Ahmad Asif. Positive Solutions of a Singular System with Two Point Coupled Boundary Conditions. Am J Appl Math. 2015;3(3-1):19-24. doi: 10.11648/j.ajam.s.2015030301.14

    Copy | Download

  • @article{10.11648/j.ajam.s.2015030301.14,
      author = {Naseer Ahmad Asif},
      title = {Positive Solutions of a Singular System with Two Point Coupled Boundary Conditions},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {3-1},
      pages = {19-24},
      doi = {10.11648/j.ajam.s.2015030301.14},
      url = {https://doi.org/10.11648/j.ajam.s.2015030301.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajam.s.2015030301.14},
      abstract = {In this paper, we study the existence of positive solutions to a system of nonlinear differential equations subject to two-point coupled boundary conditions. Further, the nonlinearities are allowed to be singular with respect to first order derivatives. An example is included to show the applicability of our result.},
     year = {2015}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Positive Solutions of a Singular System with Two Point Coupled Boundary Conditions
    AU  - Naseer Ahmad Asif
    Y1  - 2015/06/15
    PY  - 2015
    N1  - https://doi.org/10.11648/j.ajam.s.2015030301.14
    DO  - 10.11648/j.ajam.s.2015030301.14
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 19
    EP  - 24
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.s.2015030301.14
    AB  - In this paper, we study the existence of positive solutions to a system of nonlinear differential equations subject to two-point coupled boundary conditions. Further, the nonlinearities are allowed to be singular with respect to first order derivatives. An example is included to show the applicability of our result.
    VL  - 3
    IS  - 3-1
    ER  - 

    Copy | Download

  • Sections