| Peer-Reviewed

On the Existence of Positive Solution for nth Order Differential Equation for Boundary Value Problems

Received: 11 May 2017     Accepted: 6 June 2017     Published: 31 July 2017
Views:       Downloads:
Abstract

We considering the problem of solving a nonlinear differential equation in the Banach space of real functions and continuous on a bounded and closed interval. By means of the fixed point theory for a strict set contraction operator, this paper investigates the existence, nonexistence, and multiplicity of positive solutions for a nonlinear higher order boundary value problem.

Published in Mathematics and Computer Science (Volume 2, Issue 4)
DOI 10.11648/j.mcs.20170204.13
Page(s) 47-50
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), 2017. Published by Science Publishing Group

Keywords

Positive Solutions, Fixed-Point Theorem, Operator Equations, Banach Space

References
[1] Guo, D and Lakshmikantham, V., 1988, Nonlinear Problems in Abstract Cones, Academic Press, San Diego.
[2] R. P. Agarwal, M. Meehan and D. O'Regan, Fixed Point and Applications, Cambridge University Press, Cambridge, 2001.
[3] Sun, H. and Wen, W., 2006, On the Number of positive solutios for a nonlinear third order boundary value problem, International Journal of Difference Equations, 1, 165- 176.
[4] J. R. L. Webb, Positive solutions for some higher order nonlocal boundary value problems, Electronic journal of qualitative theory of differential equations spec. Ed. I, 2009 No.1, 1-14.
[5] F. Minhos and A. I. Santos, Higher order two-point boundary value problems with asym8] Qi Wang, Yanping Guo, and Yude Ji, Positive solutions for fourth-order nonlinear differential equation with integral boundary conditions, Discrete Dynamics in Nature and Society Volume 2013, (2013) 1-10.
[6] Yongping Sun and Xiaoping Zhang, Existence and nonexistence of positive solutions for fractional-order two-point boundary value problems, Advances in Difference Equations, Volume 2013 (2014) 1-11.
[7] S. N. Odda “On the existence of positive solution for the classe of nth order nonlinear differential equations” Journal of Advances in Mathematics, Vol. 9, No. 2 (2014) 1755-1759.
[8] S. N. Odda “On the existence of positive solution for the classe of nth order nonlinear differential equations” Journal of Advances in Mathematics, Vol. 9, No. 2 (2014) 1755-1759.
[9] S. N. Odda “Positive solutions of a singular 4th order two-point boundary value problem ” Journal of Natural Sciences and Mathematics, Vo 9, No.2 (2017).
[10] S. N. Odda "On The Existence Positive Solution For 5th Order Differential Equation For Boundary Value Problems" Journal of Natural Sciences and Mathematics, Vo 10, No.1 (2017).
Cite This Article
  • APA Style

    Mohamed Seddeek, Sayeda Nabhan Odda. (2017). On the Existence of Positive Solution for nth Order Differential Equation for Boundary Value Problems. Mathematics and Computer Science, 2(4), 47-50. https://doi.org/10.11648/j.mcs.20170204.13

    Copy | Download

    ACS Style

    Mohamed Seddeek; Sayeda Nabhan Odda. On the Existence of Positive Solution for nth Order Differential Equation for Boundary Value Problems. Math. Comput. Sci. 2017, 2(4), 47-50. doi: 10.11648/j.mcs.20170204.13

    Copy | Download

    AMA Style

    Mohamed Seddeek, Sayeda Nabhan Odda. On the Existence of Positive Solution for nth Order Differential Equation for Boundary Value Problems. Math Comput Sci. 2017;2(4):47-50. doi: 10.11648/j.mcs.20170204.13

    Copy | Download

  • @article{10.11648/j.mcs.20170204.13,
      author = {Mohamed Seddeek and Sayeda Nabhan Odda},
      title = {On the Existence of Positive Solution for nth Order Differential Equation for Boundary Value Problems},
      journal = {Mathematics and Computer Science},
      volume = {2},
      number = {4},
      pages = {47-50},
      doi = {10.11648/j.mcs.20170204.13},
      url = {https://doi.org/10.11648/j.mcs.20170204.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20170204.13},
      abstract = {We considering the problem of solving a nonlinear differential equation in the Banach space of real functions and continuous on a bounded and closed interval. By means of the fixed point theory for a strict set contraction operator, this paper investigates the existence, nonexistence, and multiplicity of positive solutions for a nonlinear higher order boundary value problem.},
     year = {2017}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - On the Existence of Positive Solution for nth Order Differential Equation for Boundary Value Problems
    AU  - Mohamed Seddeek
    AU  - Sayeda Nabhan Odda
    Y1  - 2017/07/31
    PY  - 2017
    N1  - https://doi.org/10.11648/j.mcs.20170204.13
    DO  - 10.11648/j.mcs.20170204.13
    T2  - Mathematics and Computer Science
    JF  - Mathematics and Computer Science
    JO  - Mathematics and Computer Science
    SP  - 47
    EP  - 50
    PB  - Science Publishing Group
    SN  - 2575-6028
    UR  - https://doi.org/10.11648/j.mcs.20170204.13
    AB  - We considering the problem of solving a nonlinear differential equation in the Banach space of real functions and continuous on a bounded and closed interval. By means of the fixed point theory for a strict set contraction operator, this paper investigates the existence, nonexistence, and multiplicity of positive solutions for a nonlinear higher order boundary value problem.
    VL  - 2
    IS  - 4
    ER  - 

    Copy | Download

Author Information
  • Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt

  • Department of Mathematics, Faculty of Women, Ain Shams University, Cairo, Egypt

  • Sections