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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
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).
[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).
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Systems and Appl., 1(1992), 271-282.
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World Scientific, (1982).
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for functional differential equations, Appl. Math. Letters, 12(1999), 63-68.
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Jour. Math. Anal. Appl., 137(1989), 59-69.
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Sturm-Liouville boundary value problems, J. Math. Anal. Appl., 304(2005),
74-89.
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boundary value problems, Appl. Math. Comput., 156(2004), 733-742.
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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://nccur.lib.nccu.edu.tw/handle/140.119/32593-
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
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
Abstract iv
中文摘要 v
1 Introduction 1
2 Second Order Ordinary Differential Equations with Various Boundary Conditions 4
2.1 Introduction 4
2.2 Existence of Positive Solution for Three Kinds of BVP 5
2.3 Remarks and An Example 9
3 Second Order Functional Differential Equations with Boundary Condition of Sturm-Liouville’s Type 12
3.1 Introduction 12
3.2 Preliminaries and Existence Results 14
3.3 Applications 19
4 High Order Ordinary Differential Equation Equipped with A Kind of Three-Point Boundary Condtion 25
4.1 Introduction 25
4.2 Preliminaries 26
4.3 Three Positive solutions 30
5 Nonlinear Second Order Elliptic Equations in An Exterior Domain 40
5.1 Introduction 40
5.2 Construction of Upper and Lower Solutions 41
References 46		zh_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
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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) for second order ordinary and delay-differential equations, J. Diff. Equations.,zh_TW
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