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July  2003, 9(4): 1049-1061. doi: 10.3934/dcds.2003.9.1049

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, South Korea, South Korea

Received  April 2002 Revised  December 2002 Published  April 2003

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.
Keywords: fixed point index., linear self-cross diffusion, Elliptic system, positive coexistence, decomposing operator.
Mathematics Subject Classification: 35J60, 92D2.
Citation: Kimun Ryu, Inkyung Ahn. Positive steady--states for two interacting species models with linear self-cross diffusions. Discrete & Continuous Dynamical Systems, 2003, 9 (4) : 1049-1061. doi: 10.3934/dcds.2003.9.1049
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