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

Pablo Álvarez-Caudevilla; Julián López-Gómez

doi:10.3934/proc.2009.2009.24

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2009, Volume 2009: 24-33. Doi: 10.3934/proc.2009.2009.24 open access

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

Pablo Álvarez-Caudevilla^1, and
Julián López-Gómez^2,

1.
Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY
2.
Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040-Madrid

Received: June 30, 2008

Revised: June 30, 2009

Published: August 2009

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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.

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Mathematics Subject Classification: Primary: 35K40, 35K50; Secondary: 35K57.

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