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研究生:陳其懋
研究生(外文):Chi- Mau Chen
論文名稱:非線性Sturm-Liouville方程週期解之存在性
論文名稱(外文):Periodic solutions of nonlinear Sturm-Liouville equations
指導教授:陳兆年
指導教授(外文):Chao-Nien Chen
學位類別:碩士
校院名稱:國立彰化師範大學
系所名稱:數學系所
學門:教育學門
學類:普通科目教育學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:英文
中文關鍵詞:非線性Sturm-Liouville週期解之存在性
相關次數:
  • 被引用被引用:2
  • 點閱點閱:211
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  • 下載下載:4
  • 收藏至我的研究室書目清單書目收藏:0
中 文 摘 要


在這篇論文裡,我們研究非線性Sturm-Liouville方程週期解的存在性。我們利用變分法來證明這些存在性定理。我們所使用的方法包含Hempel所推衍出來的片斷測地線型態論點以及在過山定理中的構思。
Abstract
In this thesis, we study the existence of periodic solutions of
nonlinear Sturm-Liouville equations. We apply variational arguments
to prove such existence results. The methods we used here include a
broken geodesic type argument derived by Hempel and an
idea in the spirit of Mountain Pass Lemma.
Section1: Introduction
Section2: Preliminaries
Section3: Broken geodesic type argument
Section4: Mountain Pass type argument
References
[1] C. N. CHEN, Multiple solutions for a class of nonlinear Sturm-Liouville problems on
the half line. J. Differential Equations 85 (1990), 236-275.
[2] J. A. HEMPEL, Multiple solutions for a class of nonlinear boundary value problems.
Indiana Univ. Math J. 20 (1971), 983-996.
[3] E. A. CODDINGTON AND N. LEVINSON, ”Theory of Ordinary Differential Equations,”
McGraw-Hill, New York, 1955
[4] J. A. HEMPEL, ”Superlinear Variational Boundary Value Problems and Nonunique-
ness,” Thesis, University of New England, Australia, 1970.
[5] K. NAKASHIMA AND K. TANAKA, Clustering layers and boundary layers in spatially
in-homogeneous phase transition problems, Ann. I. H. Poincar´e Anal. Non Lineaire
20 (2003), 107-143.
[6] M. G. CRANDALL AND P. H. RABINOWITZ, Nonlinear Sturm-Liouville eigenvalue prob-
lems and topological degree, J. Math. Mech. 29 (1970), 1083-1102.
[7] M. H. PROTTER AND H. F. WEINBERGER, ”Maximum Principles in Differential Equa-
tions,” Prentice-Hall, Englewood Cliffs, NJ, 1967.
[8] P. FELMER, S. MART´ıNEZ AND K. TANAKA, Multi-clustered high energy solutions for a
phase transition problem, preprint.
[9] P. H. RABINOWITZ, A note on a nonlinear eigenvalue problem for a class of differential
equations, J. Differential Equations 9 (1971), 536-548.

[10] P. H. RABINOWITZ, Nonlinear Sturm-Liouville problems for second order order ordi-
nary differential equations, Comm. Pure Appl. Math. 23 (1970), 939-961.
[11] R. COURANT AND D. HILBERT, ”Mathods of Mathematical Physics,” Vol. I, Inter-
science, New York, 1953
[12] Z. NEHARI, Characteristic values associated with a class of nonlinear second-order
differential equations, Acta Math. 105 (1961), 141-175.
[13] R. G. BARTLE, ”The elements of Real Analysis,” 2nd edition, John Wiley and Sons,
New York, 1976.
[14] I. M. GELFAND AND S. V. FOMIN, ”Calculus of Variations,” Prentice-Hall, New Jersey,
1963.
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