Volume no :3, Issue no: 2, November 2009

MULTIPLE POSITIVE SOLUTIONS WITH CHANGING SIGN ENERGY FOR CRITICAL LAPLACIAN SYSTEMS

Author's: Abdelaziz Ahammou and Khalid Iskafi
Pages: [153] - [170]
Received Date: December 2, 2008; Revised February 8, 20
Submitted by:

Abstract

In this paper, we are concerned with the existence of multiple positive ground state solutions to the following system, involving critical Sobolev exponents

where and verify some conditions. We show that our problem has at least two positive solutions with negative and positive energy, respectively.
By the Mountain-Pass geometry and the Ekeland variational principle, we look for Palais-Smale sequences to establish the existence of critical points for a functional associated to the problem in question.

Keywords

p-Laplacian operator, Ekeland variational principle, Mountain-Pass geometry, Palais-Smale sequences.