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

Title & Authors
A SUFFICIENT CONDITION FOR THE UNIQUENESS OF POSITIVE STEADY STATE TO A REACTION DIFFUSION SYSTEM
Kang, Joon-Hyuk; Oh, Yun-Myung;

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