摘要
研究了一类半线性反应扩散方程组在带Dirichlet边界条件下正解的存在性及稳定性.用单调解的方法给出了此解的估计,利用局部分歧理论研究了当n=1和n≠1两种情况下模型在半平凡平衡态解(θa,0)上出现的局部分歧现象,并证明了在分歧点(■,aθ,0)附近存在正解;利用稳定性理论得出当n=1时,若c、d异号,该共存解稳定;若c、d同号时,该共存解不稳定.
The existence and stability of positive solutions of a semi-linear reaction-diffusion system with Dirichlet boundary conditions are studied. An estimate of the solutions is given by the monotone method; by means of local bifurcation theory, the system bifurcations at semi-trivial solutions for two cases( n = 1 and n≠1) are studied. It is proved that positive solutions exist in some neighborhoods of (λ,θa,0). It is proved that when n = 1 and cd 〈0, the positive solution is stable.
出处
《陕西师范大学学报(自然科学版)》
CAS
CSCD
北大核心
2008年第2期15-18,共4页
Journal of Shaanxi Normal University:Natural Science Edition
基金
国家自然科学基金资助项目(10571115)
关键词
局部分歧
半平凡平衡解
稳定性
local bifurcation
semi-trivial steady-state solution
stability