一个Krasnoselski定理的推广

An Extension of Krasnoselski Theorem

主要讨论了非线性方程F（λ，u）=λu—G（u）=θ的分歧问题，其中G：X→X为非线性可微映射，X为Banach空间．在G′（θ）为紧算子，N（λ^＊I—G′（θ））＼R（λ^＊I—G′（θ））≠{θ}的条件下，利用Lyapunov-Schmidt约化过程和隐函数定理证得了方程F（λ，u）=θ在多重特征值处的分歧定理，推广了Krasnoselski的经典分歧定理．

In this paper,we mainly discuss the bifurcation problem of nonlinear equation F（/k, u） = λu - G（u） = θ, where G ： X → X is a nonlinear differential mapping, X is a Banach space. On condition that G′（θ） is compact, N（λ＊I- G′ （θ））／ R（λ^＊I- G′（θ）） ≠ {0},We apply Lyapunov-Schmidt reduction and the implicit function theorem to obtain a Bifur- cation Theorem from multiple eigenvalue of equation F（λ, u） = θ,which extend a classical bifurcation theorem by Krasnoselski.