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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/32593
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/32593


    Title: 關於幾種不同邊界值問題正解的存在性
    On the Existence of Positive Solutions for Various Boundary Value Problems
    Authors: 王勝平
    Wang,Sheng Ping
    Contributors: 王富祥
    陳天進

    Wong,Fu Hsiang
    Chen,Ten Ging

    王勝平
    Wang,Sheng Ping
    Keywords: 存在性
    正解
    邊界值
    定點定理
    上下解
    Date: 2007
    Issue Date: 2009-09-17 13:48:46 (UTC+8)
    Abstract: 在這篇論文裡,我們針對幾種不同的邊界值問題,利用不同的方法來研究正解的存在性。本文由以下幾個部分組成:首先,在外力項有某些假設的情況底下,我們用Schauder的固定點定理來探討二階常微分方程配上Sturm-Liouville或多點等等邊界值條件的正解的存在性;接著,利用Krasnoselkii的固定點定理
    考慮泛函的微分方程搭配上Sturm-Liouville型邊界條件的情況,並且給予幾個應用的法則,特別是應用在一般的常微分方程上;而對於高階的p-Laplacian方程配上另一種三點邊界條件,我們引進Leggett-Willams固定點定理的一個有名的推廣結果來證明這樣的問題有多重解;最後,利用造上下解的方法,討論二階非線性橢圓方程在一個exterior domain的情形。
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    Description: 博士
    國立政治大學
    應用數學研究所
    94751504
    96
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0094751504
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

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