Electron. J. Diff. Eqns., Vol. 2001(2001), No. 46, pp. 1-20.

A unique continuation property for linear elliptic systems and nonresonance problems

A. Anane, O. Chakrone, Z. El Allali, & I. Hadi

Abstract:
The aim of this paper is to study the existence of solutions for a quasilinear elliptic system where the nonlinear term is a Caratheodory function on a bounded domain of $\mathbb{R}^N$, by proving the well known unique continuation property for elliptic system in all dimensions: 1, 2, 3, ... and the strict monotonocity of eigensurfaces. These properties let us to consider the above problem as a nonresonance problem.

Submitted January 28, 2000. Published June 20, 2001.
Math Subject Classifications: 35J05, 35J45, 35J65.
Key Words: Unique continuation, eigensurfaces, nonresonance problem.

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A. Anane
Departement de Mathematiques et Informatique
Faculte des Sciences
Universite Mohamed 1, Oujda, Maroc
e-mail: anane@sciences.univ-oujda.ac.ma
O. Chakrone
Departement de Mathematiques et Informatique
Faculte des Sciences
Universite Mohamed 1, Oujda, Maroc
chakrone@sciences.univ-oujda.ac.ma
Z. El Allali
Departement de Mathematiques et Informatique
Faculte des Sciences
Universite Mohamed 1, Oujda, Maroc
zakaria@sciences.univ-oujda.ac.ma
Islam Eddine Hadi
Departement de Mathematiques et Informatique
Faculte des Sciences
Universite Mohamed 1, Oujda, Maroc
hadi@sciences.univ-oujda.ac.ma

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