Positive solutions bifurcating from zero solution in a Lotka-Volterra competitive system with cross-diffusion effects

被引：6
|
作者：
Zhang Cun-hua [1 ]
Yan Xiang-ping [1 ]
机构：
[1] Lanzhou Jiaotong Univ, Dept Math, Lanzhou 730070, Peoples R China
来源：
APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B | 2011年 / 26卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Lotka-Volterra competitive system; Cross-Diffusion; Positive solution; Steady state bifurcation; Stability; SPATIAL SEGREGATION; STEADY-STATES; EQUATIONS; STABILITY;
D O I：
10.1007/s11766-011-2737-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov-Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.
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页码：342 / 352
页数：11
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