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題名 | 一致方程式存在解的證明以及應用至擬線性橢圓型邊界值問題=Existence Theorems for Coincidence Equations with Applications to Quasilinear Boundary Value Problems |
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作者姓名(中文) | 宋文彬; | 書刊名 | 德明學報 |
卷期 | 12 1997.03[民86.03] |
頁次 | 頁247-255 |
分類號 | 314.74 |
關鍵詞 | Leray-schauder度論; Fredholm算子; 邊界值問題; Leray-schauder degree theory; Fredholm operator; Boundary-value problems; |
語文 | 中文(Chinese) |
中文摘要 | 本文主要利用Leray-Schauder度論來解一致方程式Lu=Fu,這�隿為一有界線性算 子,F 為一非線性算子,當然我們須轉換一致方程式成可利用 Leray-Schauder 度論的型式 ,即 u=Tu,T 為一緊緻算子, 而此抽象結果我們可用來證明某些擬線性橢圓型式邊界值問 題廣義解的存在。 |
英文摘要 | In this paper we use the Leray-Schauder degree theory to solve the coincidence equation Lu=Fu, where L:X → Y is a bouned linear operator and F: X → Y is a nonlinear operator. For convenience to use of the Leray-Schauder dagree theory we must transform the coincidence equation to an equation of fixed point type i.e., u=Tu, u �e E, T is compact for some suitable Banach space E. Our abstract results are applied to the existernce of generalized solution of quasilinear elliptic boundary value problems at resonance. |
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