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題名 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
貢獻者 王富祥<br>陳天進
Wong,Fu Hsiang<br>Chen,Ten Ging
王勝平
Wang,Sheng Ping
關鍵詞 存在性
正解
邊界值
定點定理
上下解
日期 2007
上傳時間 17-Sep-2009 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\n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。
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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).
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(1977).
[35] J. K. Hale and S. M. V. Lunel, Introduction to functional differential equations,
Springer-Verlag, New York, (1993).
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Sturm-Liouville boundary value problems, J. Math. Anal. Appl., 304(2005),
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[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.
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ordinary differential equations, Appl. Anal., 59(1995), 225-231.
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forth order two-point boundary-value problem, J. Math. Anal. Appl., 215(1997),
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fourth-order three-point boundary value problem, Taiwanese Journal of Mathematics,
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in the annulus, J. Differential Equations, 109(1994), 1-7.
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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
資料類型 thesis
dc.contributor.advisor 王富祥<br>陳天進zh_TW
dc.contributor.advisor Wong,Fu Hsiang<br>Chen,Ten Gingen_US
dc.contributor.author (Authors) 王勝平zh_TW
dc.contributor.author (Authors) Wang,Sheng Pingen_US
dc.creator (作者) 王勝平zh_TW
dc.creator (作者) Wang,Sheng Pingen_US
dc.date (日期) 2007en_US
dc.date.accessioned 17-Sep-2009 13:48:46 (UTC+8)-
dc.date.available 17-Sep-2009 13:48:46 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 13:48:46 (UTC+8)-
dc.identifier (Other Identifiers) G0094751504en_US
dc.identifier.uri (URI) https://ah.lib.nccu.edu.tw/item?item_id=33857-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 94751504zh_TW
dc.description (描述) 96zh_TW
dc.description.abstract (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\n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。zh_TW
dc.description.tableofcontents 謝辭 i\nAbstract iv\n中文摘要 v\n1 Introduction 1\n2 Second Order Ordinary Differential Equations with Various Boundary Conditions 4\n2.1 Introduction 4\n2.2 Existence of Positive Solution for Three Kinds of BVP 5\n2.3 Remarks and An Example 9\n3 Second Order Functional Differential Equations with Boundary Condition of Sturm-Liouville’s Type 12\n3.1 Introduction 12\n3.2 Preliminaries and Existence Results 14\n3.3 Applications 19\n4 High Order Ordinary Differential Equation Equipped with A Kind of Three-Point Boundary Condtion 25\n4.1 Introduction 25\n4.2 Preliminaries 26\n4.3 Three Positive solutions 30\n5 Nonlinear Second Order Elliptic Equations in An Exterior Domain 40\n5.1 Introduction 40\n5.2 Construction of Upper and Lower Solutions 41\nReferences 46zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0094751504en_US
dc.subject (關鍵詞) 存在性zh_TW
dc.subject (關鍵詞) 正解zh_TW
dc.subject (關鍵詞) 邊界值zh_TW
dc.subject (關鍵詞) 定點定理zh_TW
dc.subject (關鍵詞) 上下解zh_TW
dc.title (題名) 關於幾種不同邊界值問題正解的存在性zh_TW
dc.title (題名) On the Existence of Positive Solutions for Various Boundary Value Problemsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] R. P. Agarwal and F. H. Wong, Existence of positive solutions for higher orderzh_TW
dc.relation.reference (參考文獻) boundary value problems, Nonl. Stud., 5(1998), 15-24.zh_TW
dc.relation.reference (參考文獻) [2] R. P. Agarwal and F. H. Wong, Existence of positive solutions for non-positivezh_TW
dc.relation.reference (參考文獻) higher order BVP’s, Comp. and Appl. Math., 88(1998), 3-14.zh_TW
dc.relation.reference (參考文獻) [3] R. P. Agarwal and F. H. Wong, An application of topological transervality withzh_TW
dc.relation.reference (參考文獻) respect to non-positive higher order BVP’s, Appl. Math. and Compu., 99(1999),zh_TW
dc.relation.reference (參考文獻) 167-178.zh_TW
dc.relation.reference (參考文獻) [4] R. P. Agarwal and D. O’Regan, Some new existence results for differential andzh_TW
dc.relation.reference (參考文獻) integral equations, Nonl. Anal., 29(1997), 679-692.zh_TW
dc.relation.reference (參考文獻) [5] R. P. Agarwal and D. O’Regan, Twin solutions to singualr Dirichlet problems,zh_TW
dc.relation.reference (參考文獻) J. Math. Anal. Appl., 240(1999), 433-445.zh_TW
dc.relation.reference (參考文獻) [6] R. P. Agarwal, Boundary value problems for differential equations with deviatingzh_TW
dc.relation.reference (參考文獻) arguments, J. Math. Phy. Sci., 6(1992), 425-438.zh_TW
dc.relation.reference (參考文獻) [7] R. P. Agarwal and F. H. Wong, Upper and lower solutions for higher orderzh_TW
dc.relation.reference (參考文獻) discrete boundary value problems, Math. inequ. and appl., 1(1998), 551-557.zh_TW
dc.relation.reference (參考文獻) [8] R. P. Agarwal, F. H. Wong and S. L. Yu, Existence of solutions to (k; n¡k¡2)zh_TW
dc.relation.reference (參考文獻) discrete boundary value problems, Math. and Comp. Modell., 28(1998), 7-20.zh_TW
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dc.relation.reference (參考文獻) value problems, Applied Mathematics and Computation, 104(1999), 33-55.zh_TW
dc.relation.reference (參考文獻) [10] R. P. Agarwal, D. O’Regan and P. J. Wong, Positive solutions of Differential,zh_TW
dc.relation.reference (參考文獻) difference, and integral equations, Kluwer Academic, Dordrecht, (1999).zh_TW
dc.relation.reference (參考文獻) [11] V. Anuradha, D. D. Hai and R. Shivaji, Existence results for superlinear semipositivezh_TW
dc.relation.reference (參考文獻) BVP’s, Proc. Amer. math. Soc., 124(1996), 757-763.zh_TW
dc.relation.reference (參考文獻) [12] R. P. Avery and J. Henderson, Three symmetric positive solutions for a secondzh_TW
dc.relation.reference (參考文獻) order boundary value problem, Appl. Math. lett., 13(2000), 1-7.zh_TW
dc.relation.reference (參考文獻) [13] N. Azbelev, V. Maksimov and L. Rakhmatullina, Introduction to the theoryzh_TW
dc.relation.reference (參考文獻) of functional differential equations, (in Russian), Nauka, Moskow, (1991).zh_TW
dc.relation.reference (參考文獻) [14] Z. Bai, W. Ge and Y. Wang, Multiplicity results for some second-order fourpointzh_TW
dc.relation.reference (參考文獻) boundary-value problems, Nonl. Anal., 60(2005), 491-500.zh_TW
dc.relation.reference (參考文獻) [15] P. B. Bailey, L. F. Shampine and P. E. Waltman, Nonlinear Two-point Boundaryzh_TW
dc.relation.reference (參考文獻) Value Problems, Academic Press. New York, (1968).zh_TW
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dc.relation.reference (參考文獻) [18] A. Constantin, Existence of positive solutions of quasilinear ellitpic equations,zh_TW
dc.relation.reference (參考文獻) Bull Austral, Math. Soc., 54(1996), 147-154.zh_TW
dc.relation.reference (參考文獻) [19] A. Constantin, Positive solutions of quasilinear elliptic equations, J. Math.zh_TW
dc.relation.reference (參考文獻) Anal. Appl., 213(1997), 334-339.zh_TW
dc.relation.reference (參考文獻) [20] E. N. Dancer, On the structure of solutions of an equation in catalysis theoryzh_TW
dc.relation.reference (參考文獻) when a parameter is large, J. Diff. Eqns., 37(1980), 404-437.zh_TW
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dc.relation.reference (參考文獻) differential equations, Proc. Amer. Math. Soc., 120(1994), 743-748.zh_TW
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dc.relation.reference (參考文獻) for second order ordinary and delay-differential equations, J. Diff. Equations.,zh_TW
dc.relation.reference (參考文獻) 12(1972), 129-147.zh_TW
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