橢圓型偏微分方程式的解不存在性之探討與研究

The discussion of nonexistence solutions for the elliptic partial differential equation

楊惠文(Hui-Wen Yang)

指導教授 ： 蔡一男

大同大學/電機資訊學院/應用數學學系所/碩士(2009年)

摘要

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。

關鍵字

橢圓系統 ； 橢圓型方程式 ； 正解

並列摘要

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:

並列關鍵字

positive solution ； elliptic system ； elliptic equation

參考文獻

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