American Journal of Applied Mathematics

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Existence and Uniqueness of Weak Solution for Weighted p-bilaplacian (p-Biharmonic)

Received: 27 September 2015    Accepted: 16 November 2015    Published: 09 December 2015
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Abstract

This paper deals with the equation  in bounded domain Ω. Relying on Browder theorem, under conditions of the monotonous function f. We obtained the existence and uniqueness of weak solutions for the weighted p-bilaplacian boundary value of the form:

DOI 10.11648/j.ajam.20150306.17
Published in American Journal of Applied Mathematics (Volume 3, Issue 6, December 2015)
Page(s) 283-287
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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

Weak Solutions, p-biharmonic Operator, Browder Theorem

References
[1] G. A. Afrouzi, S. Mahdavi, Z. Naghizadeh, Existence and Uniqueness of Solution for P Laplacian Dirichlet Problem, ISSN 1749-3889 (print), 1749-3897 (online), International Journal of Nonlinear Science, Vol. 8(2009) No. 3, pp. 274-278, (Received 6 November 2008, accepted 15 July 2009).
[2] B. Al Hamzah, N. Yebari (Existence and uniqueness of weak solution for weighted p- Laplacian Steklov problem). International Journal of Innovation and Applied Studies, Vol. 11 No. 1 Apr. 2015, pp. 69-76.
[3] A.R. El Amrouss, S. El Habib, N. Tsouli, Existence of solutions for an eigenvalue problem with weight. Electronic Journal of Differential Equations, Vol. 2010(2010), No. 45, pp. 110. ISSN: 1072-6691.
[4] S. A. Khafagy, Existence and uniqueness of weak solution for weighted p-Laplacian Dirichlet problem, Vol. 3, 2011, Online ISSN: 1943-023X, Jouranal of Advanced Research in Dynamical and Control Systems.
[5] S. A. Khafagy, Existence and Uniqueness of Weak Solution for Quasilinear Elliptic (p, q)-Laplacian System. Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 8, Number 4 (2012), pp. 465475.
[6] A. El Khalil, S. Kellati A. Touzani, On the spectrum of the p-biharmonic operator. 2002-Fez conference on Partial Dikerential Equations, Electronic Journal of Dikeren- tial Equations, Conference 09, 2002, pp 161170.
[7] El. M. Hssini, M. Massar, M. Talbi and N. Tsouli, Existence of solutions for a fourth order problem at resonance. Bol. Soc. Paran. Mat. (3s.) v. 32 2 (2014): 133142.SPM ISSN-2175-1188, ISSN-00378712 in press.
[8] P. Lindqvist, Notes on the p-Laplace equation, NO-7491 Trondheim, Norway.
[9] P. Sorin Ilia_s, P-laplacien à Poids Indéfini, Vol. LVIII, No. 2/2006.
[10] E. El-zahrani , H. Serag , Existence of Weak Solutions for Nonlinear Elliptic Systems on ℜN, Electron. J. Diff. Eqns., Vol. 2006, No. 69, 1–10, 2006.
Author Information
  • University Abdelmalek Essaadi, Faculty of Sciences, Department of Mathematics, Tetouan, Morocco

  • University Abdelmalek Essaadi, Faculty of Sciences, Department of Mathematics, Tetouan, Morocco

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    Bassam Al-Hamzah, Naji Yebari. (2015). Existence and Uniqueness of Weak Solution for Weighted p-bilaplacian (p-Biharmonic). American Journal of Applied Mathematics, 3(6), 283-287. https://doi.org/10.11648/j.ajam.20150306.17

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    ACS Style

    Bassam Al-Hamzah; Naji Yebari. Existence and Uniqueness of Weak Solution for Weighted p-bilaplacian (p-Biharmonic). Am. J. Appl. Math. 2015, 3(6), 283-287. doi: 10.11648/j.ajam.20150306.17

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    AMA Style

    Bassam Al-Hamzah, Naji Yebari. Existence and Uniqueness of Weak Solution for Weighted p-bilaplacian (p-Biharmonic). Am J Appl Math. 2015;3(6):283-287. doi: 10.11648/j.ajam.20150306.17

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  • @article{10.11648/j.ajam.20150306.17,
      author = {Bassam Al-Hamzah and Naji Yebari},
      title = {Existence and Uniqueness of Weak Solution for Weighted p-bilaplacian (p-Biharmonic)},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {6},
      pages = {283-287},
      doi = {10.11648/j.ajam.20150306.17},
      url = {https://doi.org/10.11648/j.ajam.20150306.17},
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      abstract = { This paper deals with the equation  in bounded domain Ω∈. Relying on Browder theorem, under conditions of the monotonous function f. We obtained the existence and uniqueness of weak solutions for the weighted p-bilaplacian boundary value of the form: },
     year = {2015}
    }
    

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