# American Institute of Mathematical Sciences

May  2013, 12(3): 1279-1297. doi: 10.3934/cpaa.2013.12.1279

## Uniqueness of positive steady state solutions to the unstirred chemostat model with external inhibitor

 1 College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi 710062 2 School of Science, Xi'an Shiyou University, Xi'an, Shaanxi 710065, China 3 College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi 710119

Received  January 2012 Revised  August 2012 Published  September 2012

A competition model of two organisms is considered in the un-stirred chemostat-type system in the presence of an external inhibitor. Asymptotic stability properties of the trivial and semi-trivial steady state solutions are established by spectral analysis. The stability and uniqueness of positive steady state solutions are also given by Lyapunov Schmidt procedure and perturbation technique.
Citation: Hua Nie, Wenhao Xie, Jianhua Wu. Uniqueness of positive steady state solutions to the unstirred chemostat model with external inhibitor. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1279-1297. doi: 10.3934/cpaa.2013.12.1279
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##### References:
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