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研究生:楊惠文
研究生(外文):Hui-Wen Yang
論文名稱:橢圓型偏微分方程式的解不存在性之探討與研究
論文名稱(外文):The discussion of nonexistence solutions for the elliptic partial differential equation
指導教授:蔡一男
指導教授(外文):Yi-Nan Tsai
學位類別:碩士
校院名稱:大同大學
系所名稱:應用數學學系(所)
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
論文頁數:45
中文關鍵詞:橢圓系統橢圓型方程式正解
外文關鍵詞:positive solutionelliptic systemelliptic equation
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本篇論文的目標是探討方程式的解不存在性。
是個常數且K(×) 是赫德連續函數。
在第二章,我們討論方程式的解存在和不存在的問題。在第三章我們探討
橢圓型偏微分方程系統
且p 和q 是非負連續函數。我們對於(1.4)的基本假設下
有解不存在的標準。為了加強解不存在的標準,我們對於(1.4)p 和
q 是球對稱的基本假設下有解存在的定理。
The purpose of this thesis is to review some results about the elliptic equation
where s > 1 is a constant, and K(×) is a bounded Holder continuous function.
In chapter 2 we give the proofs of the existence theorems and nonexistence
results. In chapter 3 we discuss elliptic system of the form
in R ,where a, b > 0 , and p and q are nonnegative continuous functions. We give
nonexistence criteria of positive entire solutions for (1.4) under the basic assumption
ab > 1. To reinforce our nonexistence criteria, we give existence theorems of
positive entire solutions for (1.4) under the basic assumption that ab > 1 and p and q have spherical symmetry.
Keywords:
TABLE OF CONTENTS
ACKNOWLEDGMENTS i
English ii
CHINESE ABSTRACTiii
CHAPTER
I. Introduction1
II. Nonexistence Result5
III. Elliptic System20
REFERENCES37
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