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系統識別號 U0002-0207200918270700
中文論文名稱 二階p-Laplacian算子之四點邊界值問題的對稱正解存在性
英文論文名稱 The existence of symmetric positive solutions for Sturm-Liouville-like four-point boundary value problem of a second order p-Laplacian equation
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 97
學期 2
出版年 98
研究生中文姓名 蕭宇珊
研究生英文姓名 Yu-shan Shiau
學號 696190031
學位類別 碩士
語文別 中文
口試日期 2009-06-17
論文頁數 18頁
口試委員 指導教授-錢傳仁
委員-王富祥
委員-楊定揮
委員-錢傳仁
中文關鍵字 Sturm-Liouville型  p-Laplacian算子 
英文關鍵字 Sturm-Liouville-Like  p-Laplacian 
學科別分類 學科別自然科學數學
中文摘要 這篇論文是配合上解及下解(Upper and Lower Solution) 找出適當的算子,再利用 Schauder 定點定理,探討p-Laplacian算子方程在Sturm-Liouville-Like四點邊界值下對稱正解的存在性。
英文摘要 In this paper, the Sturm–Liouville-like four-point boundary value problem with a p-Laplacian operator.
By the use of Schauder fixed point theorem and upper and lower solution, we explore the p-Laplacian operator equation in the Sturm-Liouville-Like a four-point boundary value under symmetric Existence of Positive Solutions .
論文目次 目錄
一、 引言 …………………………………………… 1
二、 背景知識 ……………………………………… 2
三、 主要定理 ……………………………………… 5
四、 附錄 ………………………………………… 11
五、 參考文獻……………………………………… 17
參考文獻 1. Robert G. Bartle, The Elements of Real Analysis Second Edition, John Wiley and Sons,New York (1978).
2. Zhanbing Bai and Zengji Du, Positive solutions for some second-order four-point boundary value problems, J. Math. Anal. Appl. (2006).
3. John B. Conway, A Course in Functional Analysis Second Edition, Springer-Verlag New York Inc. (1985).
4. Z. Du, C. Xue and W. Ge, Multiple solutions for three-point boundary value problem with nonlinear terms depending on the first order derivative, Arch. Math., 84(2005), 341–349.
5. W. Feng and J.R.L. Webb, Solvability of a three-point nonlinear boundary value problems at resonance, Nonlinear Anal. 30 (1997), 3227–3238.
6. C. P. Gupta, Solvability of a three-point boundary value problem for a second order ordinary differential equation, J. Math. Anal. Appl., 168(1992), 540–551.
7. V.A. Il’in and E.I. Moiseer, Nonlocal boundary value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects, Differen. Equat. 23 (1987), 803–810.
8. V.A. Il’in and E.I. Moiseer, Nonlocal boundary value problem of the second kind for a Sturm–Liouville operator, Differen. Equat. 23 (1987), 979–987.
9. Dehong Ji, Weigao Ge and Yitao Yan, The existence of symmetric positive solutions for Sturm–Liouville-like four-point boundary value problem with a p-Laplacian operator, Applied Mathematics and Computation 189 (2007),1087–1098.
10. R. A. Khan and J. R. L. Webb, Existence of at least three solutions of a second-order threepoint boundary value problem, Nonlinear Anal., 64(2006), 1356–1366.
11. Bing Liu, Positive solutions of three-point boundary value problems for the one-dimensional p-Laplacian with infinitely many singularities, Appl. Math. Lett. 17 (2004), 655–661.
12. FuYI Li and YaJing Zhang, Multiple symmetric nonnegative solutions of second order ordinary differential equations, Appl. Math. Lett. 17 (2004), 261–267.
13. R. Ma and H. Wang, Positive solutions of a nonlinear three-point boundary value problems, J. Math. Anal. Appl., 279(2003), 216–227.
14. J. R. L. Webb, Positive solutions of some three point boundary value problems via fixed point index theory, Nonlinear Anal., 47(2001), 4319–4332.
15. F.H. Wong, T.G. Chen and S.P. Wang, Existence of positive solutions for various boundary value problem, Computers and Mathematics with Applications 56 (2008) 953–958.
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