政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32593
English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  全文笔数/总笔数 : 113648/144635 (79%)
造访人次 : 51688636      在线人数 : 625
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
搜寻范围 查询小技巧：
  • 您可在西文检索词汇前后加上"双引号"，以获取较精准的检索结果
  • 若欲以作者姓名搜寻，建议至进阶搜寻限定作者字段，可获得较完整数据
    •  进阶搜寻
    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/32593


    请使用永久网址来引用或连结此文件: https://nccur.lib.nccu.edu.tw/handle/140.119/32593


    题名: 關於幾種不同邊界值問題正解的存在性
    On the Existence of Positive Solutions for Various Boundary Value Problems
    作者: 王勝平
    Wang,Sheng Ping
    贡献者: 王富祥
    陳天進
    Wong,Fu Hsiang
    Chen,Ten Ging
    王勝平
    Wang,Sheng Ping
    关键词: 存在性
    正解
    邊界值
    定點定理
    上下解
    日期: 2007
    上传时间: 2009-09-17 13:48:46 (UTC+8)
    摘要: 在這篇論文裡，我們針對幾種不同的邊界值問題，利用不同的方法來研究正解的存在性。本文由以下幾個部分組成：首先，在外力項有某些假設的情況底下，我們用Schauder的固定點定理來探討二階常微分方程配上Sturm-Liouville或多點等等邊界值條件的正解的存在性；接著，利用Krasnoselkii的固定點定理
    考慮泛函的微分方程搭配上Sturm-Liouville型邊界條件的情況，並且給予幾個應用的法則，特別是應用在一般的常微分方程上；而對於高階的p-Laplacian方程配上另一種三點邊界條件，我們引進Leggett-Willams固定點定理的一個有名的推廣結果來證明這樣的問題有多重解；最後，利用造上下解的方法，討論二階非線性橢圓方程在一個exterior domain的情形。
    參考文獻: [1] R. P. Agarwal and F. H. Wong, Existence of positive solutions for higher order
    boundary value problems, Nonl. Stud., 5(1998), 15-24.
    [2] R. P. Agarwal and F. H. Wong, Existence of positive solutions for non-positive
    higher order BVP’s, Comp. and Appl. Math., 88(1998), 3-14.
    [3] R. P. Agarwal and F. H. Wong, An application of topological transervality with
    respect to non-positive higher order BVP’s, Appl. Math. and Compu., 99(1999),
    167-178.
    [4] R. P. Agarwal and D. O’Regan, Some new existence results for differential and
    integral equations, Nonl. Anal., 29(1997), 679-692.
    [5] R. P. Agarwal and D. O’Regan, Twin solutions to singualr Dirichlet problems,
    J. Math. Anal. Appl., 240(1999), 433-445.
    [6] R. P. Agarwal, Boundary value problems for differential equations with deviating
    arguments, J. Math. Phy. Sci., 6(1992), 425-438.
    [7] R. P. Agarwal and F. H. Wong, Upper and lower solutions for higher order
    discrete boundary value problems, Math. inequ. and appl., 1(1998), 551-557.
    [8] R. P. Agarwal, F. H. Wong and S. L. Yu, Existence of solutions to (k; n¡k¡2)
    discrete boundary value problems, Math. and Comp. Modell., 28(1998), 7-20.
    [9] R. P. Agarwal and F. H. Wong, Existence of solutions to (k; n¡k¡2) boundary
    value problems, Applied Mathematics and Computation, 104(1999), 33-55.
    [10] R. P. Agarwal, D. O’Regan and P. J. Wong, Positive solutions of Differential,
    difference, and integral equations, Kluwer Academic, Dordrecht, (1999).
    [11] V. Anuradha, D. D. Hai and R. Shivaji, Existence results for superlinear semipositive
    BVP’s, Proc. Amer. math. Soc., 124(1996), 757-763.
    [12] R. P. Avery and J. Henderson, Three symmetric positive solutions for a second
    order boundary value problem, Appl. Math. lett., 13(2000), 1-7.
    [13] N. Azbelev, V. Maksimov and L. Rakhmatullina, Introduction to the theory
    of functional differential equations, (in Russian), Nauka, Moskow, (1991).
    [14] Z. Bai, W. Ge and Y. Wang, Multiplicity results for some second-order fourpoint
    boundary-value problems, Nonl. Anal., 60(2005), 491-500.
    [15] P. B. Bailey, L. F. Shampine and P. E. Waltman, Nonlinear Two-point Boundary
    Value Problems, Academic Press. New York, (1968).
    [16] C. Bandle and M. K. Kwong, Semilinear elliptic problems in annular domains,
    J. Appl. Math. Phys., 40(1989), 245-257.
    [17] Y. S. Choi and G. S. Ludford, An unexpected stability result of the nearextinction
    diffusion flame for non-unity Lewis numbers, Q. J. Mech. Appl.
    Math., 42 part 1(1989), 143-158.
    [18] A. Constantin, Existence of positive solutions of quasilinear ellitpic equations,
    Bull Austral, Math. Soc., 54(1996), 147-154.
    [19] A. Constantin, Positive solutions of quasilinear elliptic equations, J. Math.
    Anal. Appl., 213(1997), 334-339.
    [20] E. N. Dancer, On the structure of solutions of an equation in catalysis theory
    when a parameter is large, J. Diff. Eqns., 37(1980), 404-437.
    [21] H. Dang and K. Schmit, Existence of positive solutions for semiliear elliptic
    equations in annular domain, Diff. and Integ. Equs., 7(1994) 747-758.
    [22] N. Dunford, J. T. Schwartz Linear Operators. General theory, 1, Interscience,
    (1958).
    [23] J. Ehme and J. Henderson, Functional boundary value problems and smoothness
    of solutions, Nonl. Anal., 24(1996), 139-148.
    [24] P. W. Eloe and J. Henderson, Positive solutions and nonlinear (k,n-k) conjugate
    eigenvalue problem, Diff. Equ. Dynam. Syst., 6(1998), 309-317.
    [25] L. H. Erbe and H. Wang, On the existence of positive solutions of ordinary
    differential equations, Proc. Amer. Math. Soc., 120(1994), 743-748.
    [26] L. H. Erbe, Q. K. Kong, Boundary value problems for singular second order
    functional differential equations, J. Comput. Appl. Math., 53(1994), 377-388.
    [27] W. Feng and J. R. L. Webb, Solvability of a three point nonlinear boundary
    value problems at resonance, Nonl. Anal. T.M.A., 30:6(1997), 3227-3238.
    [28] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second
    Order, Springer-Verlag, New York, (1983).
    [29] J. R. Graef and B. Yang, On a nonlinear boundary-value problem for fourthorder
    equations, Appl. Anal., 72(1999), 139-448.
    [30] J. R. Graef and B. Yang, Existence and non-existence of positive solutions of
    fourth-order nonlinear boundary-value problem, Appl. Anal., 74(2000), 201-214.
    [31] L. J. Grimm and K. Schmitt, Boundary value problems for differential equations
    with deviating arguments, Aequationes Math., 4(1970), 176-190.
    [32] G. B. Gustafson and K. Schmitt, Nonzero solutions of boundary value problems
    for second order ordinary and delay-differential equations, J. Diff. Equations.,
    12(1972), 129-147.
    [33] D. Guo and V. Lakshmikantham, Nonlinear problems in abstract cone, Academic
    Press, Orlando, FL, (1998).
    [34] J. K. Hale, Thoery of functional differential equations, Springer, New York,
    (1977).
    [35] J. K. Hale and S. M. V. Lunel, Introduction to functional differential equations,
    Springer-Verlag, New York, (1993).
    [36] J. Henderson, Singular boundary value problems for difference equations, Dynamic
    Systems and Appl., 1(1992), 271-282.
    [37] J. Henderson, Boundary value problems for functional differential equations,
    World Scientific, (1982).
    [38] J. Henderson and W. Yin, Positive solutions and nonlinear eugenvalue problems
    for functional differential equations, Appl. Math. Letters, 12(1999), 63-68.
    [39] G. L. Karakostas, K. G. Marvridis, and P. Ch. Tsamatos, Multiple positive
    solutions for a funcational second-order boundary value problem, J. Math. Anal.
    Appl., 282(2003), 567-577.
    [40] P. Kelevedjiev, Existence of solutions for two-point boundary value problems,
    Nonl. Analysis T.M.A., 22(1994), 217-224.
    [41] P. Kelevedjiev, Nonexistence of solutions for two-point boundary value problems,
    Nonl. Analysis T.M.A., 22(1994), 225-228.
    [42] V. Kolmanovskii and A. Myshkis, Applied theory of functional differential
    equations, Kluwer Academic, Dordrecht, (1992).
    [43] M. A. Krasnosekskii, Positive solutions of operations, Noordhoff, Groningen,
    (1964).
    [44] J. W. Lee and D. O’Regan, Nonlinear boundary value problems in Hilbert spaces,
    Jour. Math. Anal. Appl., 137(1989), 59-69.
    [45] Y. Li, On the existence and nonexistence of positive solutions for nonlinear
    Sturm-Liouville boundary value problems, J. Math. Anal. Appl., 304(2005),
    74-89.
    [46] X. Liu, J. Qiu and Y. Guo Three positive solutions for second-order m-point
    boundary value problems, Appl. Math. Comput., 156(2004), 733-742.
    [47] R. Ma, Positive solutions for boundary value problems of functional differential
    equations, Appl. Math. Comput., 193(2007), 66-72.
    [48] R. Y. Ma, Positive solutions of nonlinear three point boundary value problem,
    Electronic J. Diff. Equs., 34(1998), 1-8.
    [49] R. Y. Ma, Existence theorems for a second order three point boundary value
    problem, J. Math. Anal. Appl., 212(1997), 430-442.
    [50] R. Y. Ma and H. Y.Wong, On the existence of positive solutions of fourth-order
    ordinary differential equations, Appl. Anal., 59(1995), 225-231.
    [51] R. Y. Ma, J. Zhang and S. Fu, The method of lower and upper solutions for
    forth order two-point boundary-value problem, J. Math. Anal. Appl., 215(1997),
    415-422.
    [52] De-xiang Ma and Wei-gao Ge, Existence theorems of positive solutions for a
    fourth-order three-point boundary value problem, Taiwanese Journal of Mathematics,
    10:6(2006), 1557-1573.
    [53] V. Nemyckii, The fixed point method in analysis, Amer. Math. Soc. Transl.,
    34(1963), 1-37.
    [54] S. K. Ntouyas, Y. G. Sficas and P. Ch. Tsamatos, An existence principle
    for boundary value problems for second order functional differential equations,
    Nonlinear Anal., 20:3(1993), 215-222.
    [55] E. S. Noussair and C. A. Swanson, Positive solutions of quasilinear elliptic
    equations in exterior domains, J. Math. Anal. Appl., 75(1980), 121-133.
    [56] H. Wang, On the existence of positive solutions for semilinear elliptic equations
    in the annulus, J. Differential Equations, 109(1994), 1-7.
    [57] Haiyan Wang, Positive periodic solutions of functional differential equations,
    J. Differ. Equations, 202:4(2004), 354-366.
    [58] F. H. Wong, W. C. Lian, S. W. Lin and S. L. Yu Existence of periodic solutions
    of high order differential equations, Math. Computer Modelling, 21(2005), 215-
    225.
    [59] F. H. Wong, An application of Schauder’s fixed point theorem with respect to
    higher order BVPs, Proc. Amer. Math. Soc., 126(1998), 2389-2397.
    [60] F. H.Wong, W. C. Lian, S. W. Lin and S. L. Yu, Existence of periodic solutions
    of high order differential equations, Math. Computer Modelling, 21(2005), 215-
    225.
    [61] Hong-Kun Xu and E.Liz, Boundary value problems for functional differential
    equations, Nonlinear Anal., 41(2000), 971-988.
    [62] Q. Yao, Successive iteration and positive solution for nonlinear second-order
    three-point boundary value problems, Computers Math. Applic., 50(2005), 433-
    444.
    [63] B. G. Zhang and L. Z. Kong, Multiple positive solutions of a class of p-
    Laplacian equations, Annals Math., 6(2001), 1-6.
    描述: 博士
    國立政治大學
    應用數學研究所
    94751504
    96
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0094751504
    数据类型: thesis
    显示于类别:[應用數學系] 學位論文

    文件中的档案:

    档案 描述 大小格式浏览次数
    150401.pdf54KbAdobe PDF2678检视/开启
    150402.pdf26KbAdobe PDF2820检视/开启
    150403.pdf225KbAdobe PDF2831检视/开启
    150404.pdf21KbAdobe PDF2812检视/开启
    150405.pdf70KbAdobe PDF2827检视/开启
    150406.pdf46KbAdobe PDF2867检视/开启
    150407.pdf83KbAdobe PDF2914检视/开启
    150408.pdf105KbAdobe PDF2929检视/开启
    150409.pdf121KbAdobe PDF2857检视/开启
    150410.pdf90KbAdobe PDF2848检视/开启
    150411.pdf42KbAdobe PDF21160检视/开启


    在政大典藏中所有的数据项都受到原著作权保护.


    社群 sharing

    著作權政策宣告 Copyright Announcement
    1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
    The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

    2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
    NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - 回馈