Skip to content


Open Access

Existence and Nonexistence Results for a Class of Quasilinear Elliptic Systems

Boundary Value Problems20072007:085621

Received: 18 June 2007

Accepted: 20 August 2007

Published: 17 December 2007


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


Differential EquationPartial Differential EquationOrdinary Differential EquationFunctional EquationVariational Method


Authors’ Affiliations

Department of Mathematics, Faculty of Sciences, Al-Imam University, Riyadh, Saudi Arabia
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, USA


  1. Perera K: Multiple positive solutions for a class of quasilinear elliptic boundary-value problems. Electronic Journal of Differential Equations 2003, (7):5.MathSciNetGoogle Scholar
  2. Maya C, Shivaji R: Multiple positive solutions for a class of semilinear elliptic boundary value problems. Nonlinear Analysis 1999,38(4):497-504. 10.1016/S0362-546X(98)00211-9MATHMathSciNetView ArticleGoogle Scholar
  3. de Thélin F: Première valeur propre d'un système elliptique non linéaire. Comptes Rendus de l'Académie des Sciences 1990,311(10):603-606.MATHGoogle Scholar
  4. Anane A:Simplicité et isolation de la première valeur propre du -laplacien avec poids. Comptes Rendus des Séances de l'Académie des Sciences 1987,305(16):725-728.MATHMathSciNetGoogle Scholar
  5. DiBenedetto E: local regularity of weak solutions of degenerate elliptic equations. Nonlinear Analysis 1983,7(8):827-850. 10.1016/0362-546X(83)90061-5MATHMathSciNetView ArticleGoogle Scholar
  6. Trudinger NS: On Harnack type inequalities and their application to quasilinear elliptic equations. Communications on Pure and Applied Mathematics 1967,20(4):721-747. 10.1002/cpa.3160200406MATHMathSciNetView ArticleGoogle Scholar
  7. Rabinowitz PH: Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics. Volume 65. American Mathematical Society, Washington, DC, USA; 1986:viii+100.Google Scholar


© S. El Manouni and K. Perera. 2007

This article is published under license to BioMed Central Ltd. 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.