Existence and Nonexistence of Weak Positive Solution for Classes of 3 × 3 P-Laplacian Elliptic Systems

Guefaifia Rafik¹, Akrout Kamel^1, and Saifia Warda²

¹LAMIS Laboratory, Tebessa University, Tebessa, Algeria

²LANOS Laboratory, Badji Mokhtar University, Annaba, Algeria

Cite this paper:
Guefaifia Rafik, Akrout Kamel and Saifia Warda. Existence and Nonexistence of Weak Positive Solution for Classes of 3 × 3 P-Laplacian Elliptic Systems. International Journal of Partial Differential Equations and Applications. 2013; 1(1):13-17. doi: 10.12691/ijpdea-1-1-3

Abstract

In this work, we are interested to obtain some result of existence and nonexistence of large positive weak solution for the following p-laplacian system where λ, µ and ν are a positive parameter, and Ω is a bounded domain in with smooth boundary ∂Ω. The proof of the main results is based to the sub-supersolutions method.

Keywords:
Positive solutions Sub-supersolutions p-Laplacian systems

This 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]	S. Ala, G. A. Afrouzi, Q. Zhang & A. Niknam, Existence of positive solutions for variable exponent elliptic systems, Boundary Value Problems 2012, 2012:37.
[2]	G. A. Afrouzi & J. Vahidi, On critical exponent for the existence and stability properties of positive weak solutions for some nonlinear elliptic systems involving the (p, q)-Laplacian and indefinite weight function, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 121, No. 1, February 2011, pp. 83-91.
[3]	G. A. Afrouzi & Z. Valinejad, Nonexistence of result for some p-Laplacian Systems, The Journal of Mathematics and Computer Science Vol. 3 No. 2 (2011) 112-116.
[4]	J. Ali, R. Shivaji, Existence results for classes of Laplacian systems with sign-changing weight, Applied Mathematics Letters 20 (2007) 558-562.
[5]	J. Ali, R. Shivaji, Positive solutions for a class of p-Laplacian systems with multiple parameters, J. Math. Anal. Appl. 335 (2007) 1013-1019.s.
[6]	C. Chen, On positive weak solutions for a class of quasilinear elliptic systems, Nonlinear Analysis 62 (2005) 751-756.
[7]	R. Dalmasso, Existence and uniqueness of positive solutions of semilinear elliptic systems, Nonlinear Analysis 39 (2000) 559-568.
[8]	H. Dang, S. Oruganti & R. Shivaji, nonexistence of non positive solutions for a class of semilinear elliptic systems, Rocky Mountain Journal of mathematics, Volume 36, Number 6, 2006.
[9]	D. D. Hai, R. Shivaji, An existence result on positive solutions for a class of p-Laplacian systems, Nonlinear Analysis 56 (2004) 1007-1010.
[10]	P. Drˆabek & J. Hern´andez, Existence and uniqueness of positive solutions for some quasilinear elliptic problems, Nonlinear Analysis 44 (2001).
[11]	S. Haghaieghi & G. A. Afrouzi, Sub-super solutions for (p-q) Laplacian systems, Boundary Value Problems 2011, 2011:52.
[12]	R. Shivaji a & J. Ye, Nonexistence results for classes of 3 × 3 elliptic systems, Nonlinear Analysis 74 (2011) 1485-1494. 189-204.