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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Lyapunov–Schmidt reduction ： ウィキペディア英語版 Lyapunov–Schmidt reduction In mathematics, the Lyapunov–Schmidt reduction or Lyapunov–Schmidt construction is used to study solutions to nonlinear equations in the case when the implicit function theorem does not work. It permits the reduction of infinite-dimensional equations in Banach spaces to finite-dimensional equations. It is named after Aleksandr Lyapunov and Erhard Schmidt. ==Problem setup== Let :$f(x,\backslash lambda)=0\; \backslash ,$ be the given nonlinear equation, $X,\backslash Lambda,$ and $Y$ are Banach spaces ($\backslash Lambda$ is the parameter space). $f(x,\backslash lambda)$ is the $C^p$-map from a neighborhood of some point $(x\_0,\backslash lambda\_0)\backslash in\; X\backslash times\; \backslash Lambda$ to $Y$ and the equation is satisfied at this point :$f(x\_0,\backslash lambda\_0)=0.$ For the case when the linear operator $f\_x(x,\backslash lambda)$ is invertible, the implicit function theorem assures that there exists a solution $x(\backslash lambda)$ satisfying the equation $f(x(\backslash lambda),\backslash lambda)=0$ at least locally close to $\backslash lambda\_0$. In the opposite case, when the linear operator $f\_x(x,\backslash lambda)$ is non-invertible, the Lyapunov–Schmidt reduction can be applied in the following way. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lyapunov–Schmidt reduction」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.