一类具有二维零空间的非线性分歧问题分析

Analysis of a class of nonlinear bifurcation problems with two-dimensional null space

讨论了一类具有二维零空间的非线性分歧问题,运用Liapunov-Schmidt约化方法得到分歧方程,并且以一个二阶常微分方程两点边值问题为例,求出其分歧方程的近似方程,进而推得原问题平凡解枝上具有二维零空间的分歧点的类型.

One class of nonlinear bifurcation problems with two-dimensional null space is considered. The bifurcation equation is derived by using Liapunov-Schmidt reduction method.The basic idea and techniques are illustrated by a second order ordinary differential equation with two-point boundary conditions. At last,the type of bifurcation point is obtained.