`a`

On certain elliptic systems with nonlinear self-cross diffusions

Pages: 752 - 759, Issue Special, July 2003

 Abstract        Full Text (179.6K)              

Kimun Ryu - Department of Mathematics, Korea University, Jochiwon, Chung-nam 339-700, South Korea (email)
Inkyung Ahn - Department of Mathematics, Korea University, Jochiwon, Chung-nam 339-700, South Korea (email)

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.

Keywords:  nonlinear elliptic system, positive coexistence, nonlinear self-cross diffusions, fixed point index, decomposing operator.
Mathematics Subject Classification:  35J60, 92D25.

Received: July 2002;      Revised: March 2003;      Published: April 2003.