关于u″+μ(u-u^k)=0(4≤k∈Z^+)分叉的注记

A Note on Bifurcations of u″+μ(u-u^k)=0(4≤k∈Z^+)

讨论了一类反应扩散方程 u″ +μ(u -uk) =0 ,u(0 ) =u(π) =0 (4≤k∈Z+ ,μ为参数 )的分叉现象· 运用所谓基于李雅普诺夫_施密特约化的奇异理论方法 。

Bifurcations of one kind of reaction_diffusion equations, u″+μ(u-u k)=0(μ is a parameter,4≤k∈Z +),with boundary value condition u(0)=u(π)=0 are discussed. By means of singularity theory based on the method of Liapunov_Schmidt reduction, satisfactory results can be acquired.