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Journal of Applied Mathematics
Volume 1 (2001), Issue 3, Pages 91-106

A multiplicity result for a quasilinear gradient elliptic system

Département des Mathématiques et Informatique, Faculté des Sciences UCD, El Jadida BP20, Morocco

Received 9 November 2000; Revised 21 February 2001

Copyright © 2001 Hindawi Publishing Corporation. 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.


The aim of this work is to establish the existence of infinitely many solutions to gradient elliptic system problem, placing only conditions on a potential function H, associated to the problem, which is assumed to have an oscillatory behaviour at infinity. The method used in this paper is a shooting technique combined with an elementary variational argument. We are concerned with the existence of upper and lower solutions in the sense of Hernández.