International Journal of Partial Differential Equations and Applications
ISSN (Print): 2376-9548 ISSN (Online): 2376-9556 Website: http://www.sciepub.com/journal/ijpdea Editor-in-chief: Mahammad Nurmammadov
Open Access
Journal Browser
Go
International Journal of Partial Differential Equations and Applications. 2014, 2(5), 86-90
DOI: 10.12691/ijpdea-2-5-1
Open AccessArticle

Weak Solutions for a Class of (p,q) Laplacian quasilinear Elliptic System with Different Weights

Tahar Bouali1, and Rafik Guefaifiai1

1Department of Mathematics, University Tebessa, Algeria

Pub. Date: November 16, 2014

Cite this paper:
Tahar Bouali and Rafik Guefaifiai. Weak Solutions for a Class of (p,q) Laplacian quasilinear Elliptic System with Different Weights. International Journal of Partial Differential Equations and Applications. 2014; 2(5):86-90. doi: 10.12691/ijpdea-2-5-1

Abstract

Using variational methods, we study the existence of weak solutions for the degenerate quasilinear elliptic system where is a smooth bounded domain, stands for the gradient of -function the weights are allowed to vanish somewhere, the primitive is intimately related to the first eigenvalue of a corresponding quasilinear system

Keywords:
quasilinear elliptic system Palais-Smale condition mountain pass theorem existence

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  G.A. Afrouzi, S. Mahdavi and Nikolaos B. Zographopoulos, Existence of solutions for non-uniformly nonlinear elliptic systems, Electron. J. Diff. Equ., 167(2011), 1-9.
 
[2]  G.A. Afrouzi and S. Mahdavi, Existence results for a class of degenerate quasilinear elliptic systems, Lithuanian Math. J., 51 (2011), 451-460.
 
[3]  A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical points theory and applications, J. Funct. Anal., 4 (1973), 349-381.
 
[4]  L. Boccardo and D.G. De Figueiredo, Some remarks on a system of quasilinear elliptic equations, Nonlinear Diff. Equ. Appl. (NoDEA), 9 (2002), 309-323.
 
[5]  P. Caldiroli and R. Musina, On a variational degenerate elliptic problem, Nonlinear DiĀ¤. Equ. Appl. (NoDEA), 7 (2000), 187-199.
 
[6]  N.T. Chung, Existence of in nitely many solutions for degenerate and singular elliptic systems with inde nite concave nonlinearities, Electron. J. Diff. Equ., 30 (2011), 1-12.
 
[7]  N.T. Chung and H.Q. Toan, On a class of degenerate and singular elliptic systems in bounded domain, J. Math. Anal. Appl., 360 (2009), 422-431.
 
[8]  D.G.Costa, On a class of elliptic systems in , Electron. J. Diff. Equ., 7(1994), 1-14.
 
[9]  A. Djellit and S. Tas, Existence of solutions for a class of elliptic systems in involving the p-Laplacian, Electron. J. Diff. Equ., 56 (2003), 1-8.
 
[10]  P. Drabek, A. Kufner and F. Nicolosi, Quasilinear elliptic equations with degeneration and singularities, Walter de Gruyter and Co., Berlin, 1997.
 
[11]  D.D. Hai and R. Shivaji, An existence result on positive solutions of p-Laplacian systems, Nonlinear Anal., 56 (2004), 1007-1010.
 
[12]  D.W. Huang and Y.Q. Li, Multiplicity of solutions for a noncooperative p-Laplacian elliptic system in , J. Differential Equations, 215 (2005), 206-223.
 
[13]  S. Ma, Nontrivial solutions for resonant cooperative elliptic systems via computations of the critical groups, Nonlinear Analysis, 73 (2010), 3856-3872.
 
[14]  J.M.B. do O, Solutions to perturbed eigenvalue problems of the p-Laplacian in, Electron. J. Diff. Equ., 11 (1997), 1-15.
 
[15]  T.F. Wu, The Nehari manifold for a semilinear elliptic system involving sign changing weight functions, Nonlinear Analysis, 68 (2008), 1733-1745.
 
[16]  G. Zhang and Y. Wang, Some existence results for a class of degenerate semilinear elliptic systems, J. Math. Anal. Appl., 333 (2007), 904-918.
 
[17]  N.B. Zographopoulos, On the principal eigenvalue of degenerate quasilinear elliptic systems, Math. Nachr., 281 (2008), No. 9,1351-1365.
 
[18]  N.B. Zographopoulos, On a class of degenarate potential elliptic system, Nonlinear Diff. Equ. Appl. (NoDEA), 11 (2004), 191-199.
 
[19]  N.B. Zographopoulos, p-Laplacian systems on resonance, Appl. Anal., 83 (2004), 509-519.