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題名 | Existence Theorem for Nonlinear Operator Equation=非線性算子方程式定理的存在證明 |
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作者姓名(中文) | 宋文彬; | 書刊名 | 德明學報 |
卷期 | 11 1996.03[民85.03] |
頁次 | 頁361-363 |
分類號 | 314.74 |
關鍵詞 | Fredholm算子; 緊緻算子; 和Leray-schauder度論; Fredholm operator; Compact operator; Leray-schauder degree theory; |
語文 | 英文(English) |
中文摘要 | 本文主要利用Leray-Schauder度論來解如下的問題Lx=Fx,此處L為一線性,指數為零的Fredholm算子,F為一非線性緊緻算子,我們轉換原問題為一固定點問題,其所用的方法,類以J.Mawhin教授發表在J,D,E(1972, 610-636)所建立的一致性的度論理論。 |
英文摘要 | We use the Leray-Schauder degree to solve the operator equation Lx=Fx, where L: X →Y is a Fredholm operator of index zero and F:X → Y is a nonlinear compact map. Our method have the similarity with J.Mawhin's coincidence degree theory (see[2]) and also we add some sutiable conditions in the nonlinear part F to obtain a priori bound such that the classical degree theory can be well used for the original problem. Moreover we shall give some applications to nonlinear boundary value problem in the forthcoming paper. |
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