Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents
- 1 April 2003
- journal article
- Published by European Mathematical Society - EMS - Publishing House GmbH in Annales de l'Institut Henri Poincaré C, Analyse non linéaire
- Vol. 20 (2) , 341-358
- https://doi.org/10.1016/s0294-1449(02)00013-6
Abstract
The main results of this paper establish, via the variational method, the multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents under the presence of symmetry. The concentration-compactness principle allows to prove that the Palais–Smale condition is satisfied below a certain level. Résumé: Les résultats principaux de cet article établissent, via la méthode variationnelle, la multiplicité de solutions pour des problèmes elliptiques quasi-linéaires qui font intervenir l’exposant limite de Sobolev en présence de symétrie. La méthode de concentration-compacité permet de montrer que la condition de Palais–Smale est satisfaite au-dessous d’un certain niveau.This publication has 17 references indexed in Scilit:
- Existence of positive solutions for m-Laplacian equations in N involving critical Sobolev exponentsNonlinear Analysis, 1998
- Multiplicity of Positive Solutions for Some Quasilinear Elliptic Equation in RNwith Critical Sobolev ExponentJournal of Differential Equations, 1997
- Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric termTransactions of the American Mathematical Society, 1991
- Quasilinear elliptic equations involving critical Sobolev exponentsNonlinear Analysis, 1989
- A note on the problem ??u=?u+u|u|2*?2manuscripta mathematica, 1986
- An existence result for nonlinear elliptic problems involving critical Sobolev exponentAnnales de l'Institut Henri Poincaré C, Analyse non linéaire, 1985
- The Concentration-Compactness Principle in the Calculus of Variations. The limit case, Part 1Revista Matemática Iberoamericana, 1985
- Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinityNonlinear Analysis, 1983
- Positive solutions of nonlinear elliptic equations involving critical sobolev exponentsCommunications on Pure and Applied Mathematics, 1983
- Dual variational methods in critical point theory and applicationsJournal of Functional Analysis, 1973