Descripción: Fil:Eguia, M.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

Descripción: In this paper we introduce the generalized eigenvalues of a quasilinear elliptic system of resonant type. We prove the existence of infinitely many continuous eigencurves, which are obtained by variational methods. For the one-dimensional problem, we obtain an hyperbolic type function defining a region which contains all the generalized eigenvalues (variational or not), and the proof is based on a suitable generalization of Lyapunov's inequality for systems of ordinary differential equations. We also obtain a family of curves bounding by above the kth variational eigencurve. © 2006 Elsevier Inc. All rights reserved.