一些橢圓偏微分方程解的存在性與唯一性之探討

On the Existence and Uniqueness of Solutions for Some Elliptic Partial Differential Equations

陳宜榮(Yi-Jung Chen)

指導教授 ： 錢傳仁

淡江大學/理學院/數學學系博士班/博士(2013年)

https://doi.org/10.6846/TKU.2013.00167

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。

關鍵字

擬線性橢圓方程 ； Hardy-Sobolev方程 ； Dirichlet 條件 ； Robin條件 ； 奇異解

並列摘要

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.

並列關鍵字

Quasilinear elliptic equation ； Hardy-Sobolev equation ； Dirichlet condition ； Robin condition ； singular solution

參考文獻

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