Electron. J. Diff. Eqns., Vol. 2007(2007), No. 143, pp. 1-13.

Coexistence state of a reaction-diffusion system

Yijie Meng, Yifu Wang

Taking the spatial diffusion into account, we consider a reaction-diffusion system that models three species on a growth-limiting, nonreproducing resources in an unstirred chemostat. Sufficient conditions for the existence of a positive solution are determined. The main techniques is the Leray-Schauder degree theory.

Submitted May 10, 2007. Published October 25, 2007.
Math Subject Classifications: 35J55; 58J20.
Key Words: Chemostat; competition model; principal eigenvalue; maximum principle; Leray-Schauder degree.

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Yijie Meng
Department of Mathematics, Xiang Fan University
Xiang Fan 441053, China
email: yijie_meng@sina.com
  Yifu Wang
Department of Applied Mathematics
Beijing Institute of Technology, Beijing 100081, China
email: yifu_wang@163.com

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