| 一个从多重特征值出发的分歧定理 |
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| 引用本文： | 尤佳,刘萍,王玉文.一个从多重特征值出发的分歧定理[J].数学的实践与认识,2010,40(10). |
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| 作者姓名： | 尤佳 刘萍 王玉文 |
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| 基金项目： | 数学天元基金，黑龙江省青年基金 |
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| 摘 要： | 讨论非线性方程F(λ,u)=0的分歧问题,这里F:R×X→Y为非线性微分映射,X,Y为Banach空间,利用Lyapunov-Schmidt约化过程和隐函数定理证得一个从多重特征值出发的分歧定理.推广了Crandall M G与Rabinowitz P H的经典分歧定理.
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| 关 键 词： | 多重特征值 分歧理论 Lyapunov-Schmidt约化过程 隐函数定理 |
A Bifurcation Theorem from Multiple Eigenvalues |
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| YOU Jia,LIU Ping,WANG Yu-wen.A Bifurcation Theorem from Multiple Eigenvalues[J].Mathematics in Practice and Theory,2010,40(10). |
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| Authors: | YOU Jia LIU Ping WANG Yu-wen |
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| Abstract: | In this paper,we discuss the bifurcation problem of nonlinear equation F(λ,u)= 0,where F:R×X→Y is a nonlinear differential mapping,X,Y are the Banach spaces.We apply Lyapunov-Schmidt reduction and the implicit function theorem to obtain a Bifurcation Theorem from multiple eigenvalue,which extend a bifurcation theorem from simple eigenvalue by Crandall M G and Rabinowitz P H. |
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| Keywords: | multiple eigenvalues bifurcation theory Lyapunov-Schmidt reduction implicit function theorem |
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