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A unique continuation property for linear elliptic systems and nonresonance problems. (English) Zbl 0989.35048
From authors’ 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 using the well known unique continuation property for elliptic system in all dimensions and the strict monotony of eigensurfaces. These properties allow us to consider the above problem as a nonresonance problem.

MSC:
35J45 Systems of elliptic equations, general (MSC2000)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J65 Nonlinear boundary value problems for linear elliptic equations
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