系統識別號 | U0002-0506201310231100 |
---|---|
DOI | 10.6846/TKU.2013.00167 |
論文名稱(中文) | 一些橢圓偏微分方程解的存在性與唯一性之探討 |
論文名稱(英文) | On the Existence and Uniqueness of Solutions for Some Elliptic Partial Differential Equations |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 數學學系博士班 |
系所名稱(英文) | Department of Mathematics |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 101 |
學期 | 2 |
出版年 | 102 |
研究生(中文) | 陳宜榮 |
研究生(英文) | Yi-Jung Chen |
學號 | 894150068 |
學位類別 | 博士 |
語言別 | 英文 |
第二語言別 | |
口試日期 | 2013-05-21 |
論文頁數 | 66頁 |
口試委員 |
指導教授
-
錢傳仁(chuanjen@mail.tku.edu.tw)
委員 - 錢傳仁(chuanjen@mail.tku.edu.tw) 委員 - 郭滄海(thkuo06@gmail.com) 委員 - 陳建隆(chern@math.ncu.edu.tw) 委員 - 郭忠勝(jsguo@mail.tku.edu.tw) 委員 - 張茂盛(mschang@math.fju.edu.tw) 委員 - 陳功宇(kychen@mail.tku.edu.tw) |
關鍵字(中) |
擬線性橢圓方程 Hardy-Sobolev方程 Dirichlet 條件 Robin條件 奇異解 |
關鍵字(英) |
Quasilinear elliptic equation Hardy-Sobolev equation Dirichlet condition Robin condition singular solution |
第三語言關鍵字 | |
學科別分類 | |
中文摘要 |
在本論文中我們將探討擬線性橢圓方程在Dirichlet 和 Robin 條件下,解的存在性問題;更進一步,我們在Robin 條件下得到解的唯一性。同時,我們對Hardy-Sobolev方程作了徑對稱解的研究,得到在上臨界的條件下最多僅有一個奇異解。 |
英文摘要 |
In this thesis, we study the existence of solutions to quasilinear elliptic equations with Dirichlet and Robin conditions, and the uniqueness of solutions under Robin conditions. Also, we investigate the radial symmetric solutions for a Hardy-Sobolev equation and derive the result that there exists at most one positive radial symmetric singular solution for the supercritical case. |
第三語言摘要 | |
論文目次 |
Contents Chapter 1 Introduction………………………………………………1 Chapter 2 Quasilinear Elliptic Equations with Dirichlet Conditions………………………………………………………………5 2.1 The Maximum Principl……………………………………………9 2.2 The Estimate……………………………………………………13 2.3 The Existence of Strong Solutions…………………………15 Chapter 3 Quasilinear Elliptic Equations with Robin Conditions ……………………………………………………………31 3.1 The Comparison Principle ……………………………………34 3.2 and Estimates………………………………………………38 3.3 The Existence and Uniqueness of Solutions in ………41 Chapter 4 Hardy-Sobolev Equations………………………………45 4.1 Asymptotic Behavior s…………………………………………46 4.2 The Uniqueness of Positive Radial Singular Solutions………………………………………………………………56 Appendix A Basic Notations and Fixed Point Theorems………60 A.1 Basic Notations…………………………………………………60 A.2 Fixed Point Theorems……………………………………… …62 Bibliography …………………………………………………………63 |
參考文獻 |
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