A unique continuation property for linear elliptic systems and nonresonance problems

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.

Keywords

• Unique continuation
• eigensurfaces
• nonresonance problem.