Coexistence states of a three-species cooperating model with diffusion

Abstract

In this article, a Lotka--Volterra three-species time-periodic mutualism model with diffusion is investigated. Some sufficient conditions for the existence and estimates of coexistence states are established. Meanwhile, with the assistance of functional analysis methods, some sufficient or necessary results for the existence of positive steady state of the model are presented. Our approach to the discussion is mainly based on the skill of sub- and super-solutions for a general reaction--diffusion system.

Keywords:

• cooperating model
• coexistence states
• sub- and super-solution

AMS Subject Classifications:

• 92D25
• 93C20
• 35K57

Acknowledgements

This study was supported by the National Science Foundation of China (10971124) and the Ph.D. specialized grant of Ministry of Education of China (200807180004).