Open Access Research Article

Existence and Nonexistence Results for a Class of Quasilinear Elliptic Systems

Said El Manouni1* and Kanishka Perera2

Author Affiliations

1 Department of Mathematics, Faculty of Sciences, Al-Imam University, P.O. Box 90950, Riyadh 11623, Saudi Arabia

2 Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA

For all author emails, please log on.

Boundary Value Problems 2007, 2007:085621  doi:10.1155/2007/85621

The electronic version of this article is the complete one and can be found online at:

Received:18 June 2007
Accepted:20 August 2007
Published:17 December 2007

© 2007 El Manouni and Perera

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Using variational methods, we prove the existence and nonexistence of positive solutions for a class of -Laplacian systems with a parameter.


  1. Perera, K: Multiple positive solutions for a class of quasilinear elliptic boundary-value problems. Electronic Journal of Differential Equations.(7), 5 (2003)

  2. Maya, C, Shivaji, R: Multiple positive solutions for a class of semilinear elliptic boundary value problems. Nonlinear Analysis. 38(4), 497–504 (1999). Publisher Full Text OpenURL

  3. de Thélin, F: Première valeur propre d'un système elliptique non linéaire. Comptes Rendus de l'Académie des Sciences. 311(10), 603–606 (1990)

  4. Anane, A: Simplicité et isolation de la première valeur propre du -laplacien avec poids. Comptes Rendus des Séances de l'Académie des Sciences. 305(16), 725–728 (1987). PubMed Abstract | Publisher Full Text OpenURL

  5. DiBenedetto, E: local regularity of weak solutions of degenerate elliptic equations. Nonlinear Analysis. 7(8), 827–850 (1983). Publisher Full Text OpenURL

  6. Trudinger, NS: On Harnack type inequalities and their application to quasilinear elliptic equations. Communications on Pure and Applied Mathematics. 20(4), 721–747 (1967). Publisher Full Text OpenURL

  7. Rabinowitz, PH: Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics,p. viii+100. American Mathematical Society, Washington, DC, USA (1986)