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研究生:黃瑛鳳
研究生(外文):Ying-fong Hwang
論文名稱:域指數與域變換
論文名稱(外文):Domain Transformations and Indexes of Domains
指導教授:王懷權
指導教授(外文):Hwai-Chiuan Wang
學位類別:碩士
校院名稱:國立清華大學
系所名稱:數學系
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:2004
畢業學年度:92
語文別:英文
論文頁數:29
中文關鍵詞:半線性橢圓方程域指數
外文關鍵詞:semilinear elliptic equationsindexes of domains
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在這論文裡,我們將習得巴萊斯麥爾的一些定理,且我們將定義何謂域指數。接下來,我們就是要來看看一些區域經過變換後,他的域指數會有什麼變化?最後,我們將利用所得之結果去證明一些半線性橢圓方程的解的存在性。
In this thesis, we study the Palais Smale theory and define the index of domains. Then we study the indexes of transformed domains. We then apply our theory to assert the existence of solutions of semilinear elliptic equations.
Adams, R. A., Sobolev space, Academic Press, New York 1975.
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CW : K. -J. Chen and H. -C. Wang, A necessary and sufficient condition for Palais-Smale conditions, SIAM J. Math. Anal., 31 (1999), 154-165.
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L1 : P. -L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. I, II, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), 109-145; 223-283.
L2 : P. -L. Lions, The concentration-compactness principle in the calculus of variations. The limit case. I, II, Rev. Mat. Iberoamericana, 1, No. 1 (l 985), 145-20 1; No. 2 (1985), 45-121.
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R2 : P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, Regional Conference Series in Mathematics, American Mathematical Society, 1986.
Stu : C. A. Stuart, Bifurcation in L^{p}(R^{N}) for a semilinear elliptic equation, Proc. London Math. Soc., 45 (1982), 169-192.
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W1 : H. -C. Wang, Palais-Smale approachs to semilinear elliptic equations in unbounded domains, Preprint.
Wi : M. Willem, Minimax theorems, Birkhauser Verlag, Basel, 1996.
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