Skip to main content


Existence and Nonexistence Results for a Class of Quasilinear Elliptic Systems

Article metrics

  • 611 Accesses


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



  1. 1.

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

  2. 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)00211-9

  3. 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.

  4. 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.

  5. 5.

    DiBenedetto E: local regularity of weak solutions of degenerate elliptic equations. Nonlinear Analysis 1983,7(8):827-850. 10.1016/0362-546X(83)90061-5

  6. 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.3160200406

  7. 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.

Download references

Author information

Correspondence to Said El Manouni.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article


  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Variational Method