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研究生:林家宇
研究生(外文):LIN,CHIA-YU
論文名稱:奇異橢圓方程正解的多解性
論文名稱(外文):Multiplicity of positive solutions for singular elliptic equations
指導教授:吳宗芳
指導教授(外文):WU,TSUNG-FANG
口試委員:吳宗芳郭岳承林英杰
口試委員(外文):WU,TSUNG-FANGKUO,YUEH-CHENGLIN,YING-CHIEH
口試日期:2019-11-22
學位類別:碩士
校院名稱:國立高雄大學
系所名稱:應用數學系碩博士班
論文種類:學術論文
論文出版年:2020
畢業學年度:108
語文別:英文
論文頁數:55
中文關鍵詞:半線性橢圓問題凹凸非線性變分法深井勢
外文關鍵詞:Semilinear elliptic problemsConcave-convex nonlinearitiesVariational methodsSteep potential
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在這篇文章中,我們探討涉及凹凸非線性的不定半線性橢圓方程正解的存在性與多解性,並且我們假設函數f,g和V滿足適當的條件。

In this paper, we study the existence, multiplicity of positive solutions for the indefinite semilinear elliptic equations involving concave-convex nonlinearities. We assume that the functions f,g and V satisfy suitable conditions with the potential V and the weight function g without the assumptions of infinite limits.

1Introduction
2 Preliminaries
2.1 Inequalities
2.1.1 Hölder inequality
2.1.2 Hardy inequality
2.1.3 Sobolev inequality
2.2 Variational methods and Theorems
2.3 Implicit Function Theorem
2.4 Mean Value Theorem
2.5 Brezis-Lieb Lemma
2.6 Variational Settings
3 Proof of Theorem 1.1
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