2003, 2003(Special): 752-759. doi: 10.3934/proc.2003.2003.752

On certain elliptic systems with nonlinear self-cross diffusions

1. 

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

Received  July 2002 Revised  March 2003 Published  April 2003

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.
Citation: Kimun Ryu, Inkyung Ahn. On certain elliptic systems with nonlinear self-cross diffusions. Conference Publications, 2003, 2003 (Special) : 752-759. doi: 10.3934/proc.2003.2003.752
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