Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/32593
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
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。
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
資料類型: thesis
Appears in Collections:學位論文

Files in This Item:
File Description SizeFormat
150401.pdf54.41 kBAdobe PDF2View/Open
150402.pdf26.92 kBAdobe PDF2View/Open
150403.pdf225.87 kBAdobe PDF2View/Open
150404.pdf21.4 kBAdobe PDF2View/Open
150405.pdf70.82 kBAdobe PDF2View/Open
150406.pdf46.51 kBAdobe PDF2View/Open
150407.pdf83.18 kBAdobe PDF2View/Open
150408.pdf105.91 kBAdobe PDF2View/Open
150409.pdf121.68 kBAdobe PDF2View/Open
150410.pdf90.92 kBAdobe PDF2View/Open
150411.pdf42.23 kBAdobe PDF2View/Open
Show full item record

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.