一个具有二维零空间的跨越式分歧定理

THE TRANSCRITICAL BIFURCATION THEOREM FROM TWO-DIMENSIONAL KERNEL

讨论带有参数的非线性方程F(,λu)=0的分歧问题,其中F:×X→Y为非线性微分映射,X、Y为Banach空间,利用Lyapunov-Schm idt约化过程和隐函数定理,证明了一个Fu(λ*,0)的零空间为二维的跨越式分歧定理.

This article discusses the bifurcation probh,m of nonlinear equation with parameter F（λ ,u） = 0, where F：R×X→Y is a nonlinear differential map, and X, Y are Banach spaces. Using Lyapunov - Schmidt reduction and the implicit unction theorem to prove a transcritical bifurcation theorem which kernel of derivative operator is two- dimensional.