# A SUFFICIENT CONDITION FOR THE UNIQUENESS OF POSITIVE STEADY STATE TO A REACTION DIFFUSION SYSTEM

• Kang, Joon-Hyuk ;
• Oh, Yun-Myung
• Published : 2002.05.01
• 93 22

#### Abstract

In this paper, we concentrate on the uniquencess of the positive solution for the general elliptic system $\Delta$u+u($g_1$(u)-$g_2$(v))=0 $\Delta$u+u($h_1$(u)-$h_2$(v))=0 in$R_{+}$ $\times$ $\Omega$, $u\mid\partial\Omega = u\mid\partial\Omega = 0$. 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.

#### Keywords

Lotka Voltera competition model;coexistence state

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