Positive steady--states for two interacting species models with linear self-cross diffusions

Kimun Ryu; Inkyung Ahn

doi:10.3934/dcds.2003.9.1049

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2003, Volume 9, Issue 4: 1049-1061. Doi: 10.3934/dcds.2003.9.1049

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Positive steady--states for two interacting species models with linear self-cross diffusions

Kimun Ryu^1, and
Inkyung Ahn^1,

1.
Department of Mathematics, Korea University, Jochiwon, Chung-nam 339-700

Received: March 31, 2002

Revised: November 30, 2002

Published: June 2003

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Abstract

In this paper, we discuss the positive steady-state existence for predator-prey and competing interaction systems between two species with linear self-cross diffusions. The methods employed are the decomposing operators and the theory of fixed point index on cones in a Banach space. We give sufficient conditions for the existence of positive solutions. The conditions are given in terms of the signs of the principal eigenvalues of certain differential operators.

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Mathematics Subject Classification: 35J60, 92D25.

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