On certain elliptic systems with nonlinear self-cross diffusions

Kimun Ryu; Inkyung Ahn

doi:10.3934/proc.2003.2003.752

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2003, Volume 2003: 752-759. Doi: 10.3934/proc.2003.2003.752 open access

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On certain elliptic systems with nonlinear self-cross diffusions

Kimun Ryu^1, and
Inkyung Ahn^1,

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

Received: June 30, 2002

Revised: February 28, 2003

Published: March 2003

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Abstract

We investigate the positive coexistence to certain strongly-coupled nonlinear elliptic systems with self-cross diffusions under homogeneous Robin boundary conditions. Competing interactions between two species are considered. Conditions of the positive coexistence to self-cross diffusive systems can be expressed in terms of the spectral property of differential operators of nonlinear Schrödinger type which reflect the influence of the domain and nonlinearity in the system. Decoupling method and nonlinear fixed point theorem are employed.

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Mathematics Subject Classification: 35J60, 92D25.

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