A SUFFICIENT CONDITION FOR THE UNIQUENESS OF POSITIVE STEADY STATE TO A REACTION DIFFUSION SYSTEM Kang, Joon-Hyuk; Oh, Yun-Myung;
In this paper, we concentrate on the uniquencess of the positive solution for the general elliptic system u+u((u)-(v))=0 u+u((u)-(v))=0 in , . This system is the general model for the steady state of a competitive interacting system. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.