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研究生:陳秀婷
研究生(外文):Siou-Ting Chen
論文名稱:奇異橢圓方程式解的特性
論文名稱(外文):Properties of solutions of a singular elliptic equation
指導教授:徐淑裕
指導教授(外文):Shu-Yu Hsu
口試委員:陳文豪潘志祥
口試委員(外文):Wen-hao ChenChi-Cheung Poon
口試日期:2010-06-18
學位類別:碩士
校院名稱:國立中正大學
系所名稱:數學研究所
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:2010
畢業學年度:99
語文別:英文
論文頁數:34
中文關鍵詞:奇異橢圓方程式
外文關鍵詞:singular elliptic equation
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This paper is devoted to a class of elliptic problems

with 0 < u(x) < 1 in a bounded domain
 RN(N  1): Hence  and p are positive
parameters and f(x) 2 C(
) is a nonnegative function. By the sub-super solutions
method we show that there exists a critical parameter  = (; p; f) such that (S)
has at least one solution including a unique minimal solution for  2 (0; ) and no
solution for  > : Moreover we get the rigorous bounds on : We also discuss
properties of minimal solutions of (S) including regularity and monotonicity.
1 Introduction.

2 The pull-in voltage.
2-1 Existence of the pull-in voltage.
2-2 Monotonicity results for pull-in voltage.

3 Estimates for the pull-in voltage.
3.1 Lower bounds for λ*
3.2 Upper bounds for λ*

4 The branch of minimal solutions.
4-1 Spectral properties of minimal solutions.
References
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[2] C. Bandle, Isoperimetric inequalities and applications, in: Monographs and Studiesin Mathematics, Pitman, Boston, MA, London, 1980.
[3] D. Bernstein, P. Guidotti, J.A. Pelesko, Analytic and numerical analysis of elec-trostatically actuated MEMS devices, Proc. Model. Simul. Microsyst. 2000 (2000)489-492.
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sources, Arch. Ration. Mech. Anal. 49 (1973) 241-268.
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[13] M.G. Crandall, P.H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Ration. Mech. Anal. 52 (1973) 161-180.
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[21] S. Filippas, R.V. Kohn, Rened asymptotics for the blow up of ut
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