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

Bassam Al-Hamzah; Naji Yebari

doi:doi:10.11648/j.ajam.20150306.17

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

Bassam Al-Hamzah, Naji Yebari

Published in American Journal of Applied Mathematics (Volume 3, Issue 6)

Received: 27 September 2015 Accepted: 16 November 2015 Published: 9 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:

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

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 ℜ^N, Electron. J. Diff. Eqns., Vol. 2006, No. 69, 1–10, 2006.

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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},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150306.17},
  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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TY  - JOUR
T1  - Existence and Uniqueness of Weak Solution for Weighted p-bilaplacian (p-Biharmonic)
AU  - Bassam Al-Hamzah
AU  - Naji Yebari
Y1  - 2015/12/09
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150306.17
DO  - 10.11648/j.ajam.20150306.17
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 283
EP  - 287
PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.ajam.20150306.17
AB  -  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: 
VL  - 3
IS  - 6
ER  -

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Author Information

Bassam Al-Hamzah

University Abdelmalek Essaadi, Faculty of Sciences, Department of Mathematics, Tetouan, Morocco
Naji Yebari

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

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APA Style

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

Copy | Download

@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},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150306.17},
  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}
}

Copy | Download

TY  - JOUR
T1  - Existence and Uniqueness of Weak Solution for Weighted p-bilaplacian (p-Biharmonic)
AU  - Bassam Al-Hamzah
AU  - Naji Yebari
Y1  - 2015/12/09
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150306.17
DO  - 10.11648/j.ajam.20150306.17
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 283
EP  - 287
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150306.17
AB  -  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: 
VL  - 3
IS  - 6
ER  -

Copy | Download