Characterizing the existence of coexistence states in a class of cooperative systems

Pages: 24 - 33, Issue Special, September 2009

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Pablo Álvarez-Caudevilla - Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom (email)
Julián López-Gómez - Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040-Madrid, Spain (email)

Abstract: This paper characterizes the existence of coexistence states for a class of sublinear elliptic cooperative systems with a linear equation and the other non-linear, but yet linear on a subdomain of the underlying domain. The analysis of this problem is imperative for ascertaining the dynamics of wider general classes of cooperative systems with spatially heterogeneous nonlinearities, like those introduced in López-Gómez & Molina-Meyer [10] for weakly coupled systems. Our characterization relies upon a spectral bound associated to a certain non-local second order differential operator, which has not been previously documented in the literature.

Keywords:  Coexistence states, cooperative systems, spectral bound
Mathematics Subject Classification:  Primary: 35K40, 35K50; Secondary: 35K57

Received: July 2008;      Revised: July 2009;      Published: September 2009.