| 刘焱南,刘萍,王玉文.非单特征值的广义分歧定理[J].数学年刊A辑,2011,32(1):83~88 |
| 非单特征值的广义分歧定理 |
| The Generalized Bifurcation Theorem from Multiple Eigenvalues |
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| DOI： |
| 中文关键词: 非单特征值 Lyapunov-Schmidt约化过程 分歧 |
| 英文关键词:Multiple eigenvalue The Lyapunov-Schmidt reduction Bifurcation |
| 基金项目:国家自然科学基金(No.10671049); 数学天元基金(No.10926060); 黑龙江省青年基金(No.QC2009C73)资助的项目 |
| Author Name | Affiliation | E-mail | | LIU Yannan | Y.Y.Tseng Functional Analysis Research Center,School of Mathematical Sciences,Harbin Normal University,Harbin 150025,China. | liuyannan0920@163.com | | LIU Ping | Y.Y.Tseng Functional Analysis Research Center,School of Mathematical Sciences,Harbin Normal University,Harbin 150025,China. | liuping506@gmail.com | | WANG Yuwen | Y.Y.Tseng Functional Analysis Research Center,School of Mathematical Sciences,Harbin Normal University,Harbin 150025,China. | wangyuwen1950@yahoo.com.cn |
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| 中文摘要: |
| 讨论了抽象算子方程$F(\lambda,u)=0$的局部分歧问题, 其中$F:\mathbb{R} \times X \rightarrow Y$是一个$\mathcal{C}^{2}$微分映射, $\lambda$是参数, $X,Y$为Banach空间.
利用Lyapunov-Schmidt约化过程及偏导算子$F_{u}(\lambda^{*},0)$的有界线性广义逆, 在$\dim N(F_{u}(\lambda^{*},0)) \geq {\rm codim}\, R(F_{u}(\lambda^{*},0))=1$的条件下,
证明了一个广义跨越式分歧定理. 当参数空间的维数等于值域余维数时, 应用同样的方法又得到了多参数方程的抽象分歧定理. |
| 英文摘要: |
| The authors discuss the local bifurcation problem of the abstract operator equation $F(\lambda,u)=0$, where $F:\mathbb{R} \times X \rightarrow Y$
is a $\mathcal{C}^{2}$ differential mapping, $\lambda$ is a parameter and $X,Y$ are Banach spaces. By the Lyapunov-Schmidt reduction and the
bounded linear generalized inverse of $F_{u}(\lambda^{*},0)$, a generalized transcritical bifurcation theorem is obtained under the assumption that
$\dim N(F_{u}(\lambda^{*},0)) \geq {\rm codim}\, R(F_{u}(\lambda^{*},0))=1$. When the dimension of parameter
space is equal to the codimension of range space, the authors get an abstract bifurcation theorem of the equation with
multiparameter by applying the same method. |
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