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研究生: 林忠慶
Zhon-qing Lin
論文名稱: 在N維實數域之雙調和微分方程
Biharmonic equation in R^n
指導教授: 陳建隆
Jann-Long Chern
口試委員:
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系
Department of Mathematics
畢業學年度: 92
語文別: 英文
論文頁數: 15
外文關鍵詞: Biharmonic
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  • 在這篇論文裡,主要在探討偏微分方程解的存在與否。我們首先證明解的存在性,緊接著再去探討某些特定的條件下解的存在性與否,我們可以發現在某些特定的條件下,偏微分方程解並不存在。


    Contents 1. Introduction …………………………………… 1 2. Theorems ……………………………………… 1 3. Proof of Theorems …………………………… 4 4. References …………………………………… 11

    References
    [1]WEI-MING NI.On the Elliptic Equation u(x)+k(x)u(n+2)(n−2) (x) = 0 its Generalizations,and Applications in Geometry.Indiana University Mathematics Journal,Vol.31,No.4(1982).
    [2]Manabu Naito.A note on bounded positive entire solutions of semilinear elliptic equations.Hiroshima Math.J.14(1984),211-214.
    [3]Kuo-Shung Cheng and Jenn-Tsann Lin. On the elliptic equations u = K(x)u and
    u = K(x)e2u.Transactions of the american mathtical society.Volume304,Number 2,December1987.
    [4]Guozhen Lu.Juncheng Wei.Xingwang Xu.On Conformally Invariant Equation
    (− )pu − K(x)u N+2p N−2p = 0 and Its Generalizations.Annali Di Matematica Pura ed applicata(IV),Vol.CLXXIX(2001),pp.309-329.
    [5]Ezzat S.Noussair1,Charles A.Swanson2 and Yang Jianfu3.Transcritical Biharmonic in Rn.Funkcialaj Ekvacioj,35(1992)533-543.
    [6]Takabsi Kusano1 and Charles A.Swanson2.Positiveentire solutions of semilinear biharmonic equations.Hiroshima Math.J.17(1987),13-28.
    [7]Charles A.Swanaon and Lao Sen Yu.Radial Polyharmonic Problems in Rn.Journal
    of mathematical analysis and applications 174,461-466(1993).
    [8]Robert Dalmasso.Solutions Positives Globales d’une Equation Biharmonique Surlineaire. Funkcialaj Ekavacioj.33(1990)475-492.
    [9]Yasuhiro Furusho, Saga,and Kusano Takabsi, Fukuoka.A Supersolution-Subsolution Method For Nonlinear Biharmonic Equations In Rn.Czechoslovak Mathematical Journal,47(122)(1997).Praha.
    [10]Kuo-Shung Cheng and Chern Jann-Long.Existence of Positive Entire Solutions of Some Semilinear Elliptic Equations.Journal of Di erentions 98,169-180(1992).
    [11]Chang-Shou Lin.A classification of solutions of a conformally invariant fourth order equation in Rn.Comment.Math.Helv.73(1998)206-231.

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