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研究生:邱瓊誼
研究生(外文):Chiung-Yi Chiu
論文名稱:愛思特般理翁域的描述及其應用
論文名稱(外文):Characterization of Esteban—Lions Domains with Applications
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:2002
畢業學年度:90
語文別:英文
論文頁數:38
中文關鍵詞:愛思特般理翁域
外文關鍵詞:Esteban-Lions domain
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  • 被引用被引用:0
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  • 下載下載:7
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在這篇論文裡,我們介紹愛思特般理翁域,並證明解的存在性在加了擾動後的愛思特般理翁域上。

In this thesis, we characterize the Esteban—Lions domains and prove the existence of solutions of equation (1) in a perturbation of an Esteban—Lions domain.

1.Introduction 1
2.Esteban—Lions Domains and Large Domains 2
3.Nonexistence in the Esteban—Lions Domains 7
4.Indexes of Domains 20
5.Palais Smale Condition 25
6.Existence of Solutions 35
References 37

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Berestycki, H. and Lions, P. L., Nonlinear scalar field equations. I. Existence of ground state, Arch. Rat. Mech. Anal., 82(1983), 313-345.
Brezis, H., Analyse Fonctionnelle, Theorie et Applications, Masson, Paris, 1983.
Brezis, H. and Lieb, E. H.,\ A relation between pointwise convergence of functions and convergence of functionals,\ Proc. Amer Math. Soc. 88 (1983), 486-490.
Brezis, H. and Nirenberg, L., Remarks on finding critical points, Comm. Pure Appl. Math., 44(1991), 939-963.
Chen M. C., Lin H. L., and Wang H. C., Vitali convergence theorem and Palais Smale conditions, will appear in Differential and Integral\ Equations.
Chen, C. N. and Tzeng, S. Y., Some properties of Palais-Smale sequences with applications to elliptic boundary value problems, Elec. Jour. of Diff. Eqns., Vol. 1999(1999), No. 17, 1$-$29.
Chen, K. J. and Wang, H. C., A necessary and sufficient condition for Palais-Smale conditions, SIAM Journal on Math. Anal., 31(1999), 154-165.
Esteban, M. J. and Lions, P. L., Existence and non-existence results for semilinear elliptic problems in unbounded domains, Proc. R. S. Edinburgh, 93A(1982), 1-12.
Gilbarg, D. and Trudinger, N. S., Elliptic Partial Differential Equations of Second order, Springer-Verlag, New York, 1983.
Heinz, E, \"{U}ber die Eindeutigkeit beim Cauchyschen Anfangswertproblem einer elliptischen Differentialgleichung zweiter Ordnung, Nachr. Akad. Wiss. G\"{o}ttingen, 1(1955), 1-12.
Lien, W. C., Tzeng, S. Y. and Wang, H. C., Existence of solutions of semilinear elliptic problems on unbounded domains, Diff. and Integ. Eqns., 6(1993), 1281-1298.
Protter, M. H., Unique continuation for elliptic equations, 81-91.
Stuart, C. A., Bifurcation in L^p for a semilinear elliptic equation, Proc. London Math. Soc. 45(1982), 169-192.
Struwe, M., Variational methods, Springer-Verlag, Bertin-Heidelberg, Second edition, 1996.
Wang, H. C., A Palais$-$Smale approach to problems in Esteban-Lions domains with holes, Trans. Amer. Math. Soc., 352(2000), 4237-4256.
Willem, M.,\ Minimax theorems, Birkhauser Verlag, Basel, 1996.
Zeidler, E. Nonlinear Functional Analysis and its Applications II/A, Springer-Verlag, New York, 1989.

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