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研究生:龔凡凱
研究生(外文):Fan-Kai Kung
論文名稱:二階邊界值問題解的存在性
論文名稱(外文):Existence of Solutions for Second Order Boundary Value Problems
指導教授:王富祥
指導教授(外文):Fu-Hsiang Wong
學位類別:碩士
校院名稱:國立臺北教育大學
系所名稱:數學暨資訊教育學系(含數學教育碩士班)
學門:教育學門
學類:普通科目教育學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:英文
論文頁數:13
中文關鍵詞:特徵值二階邊界值問題定點定理
外文關鍵詞:Eigenvalue problemsgreen''s functionconefixed point index
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對於下列的微分方程,λ是一個參數,我們在錐體中利用定點定理得到:當λ、f滿足某些適當的邊界條件,則此微分方程存在正解。
u"+λf(t,u)=0, 0<t<1.
We use a fixed point theorem in a cone to obtain the existence of positive solutions of the differential equation
u"+λf(t,u)=0, 0<t<1.
with some suitable boundary conditions, where is a parameter.
1.Introduction..........P1
2.Main Results..........P3
3.Examples..............P11
4.References............P13
[1] C. V. Coffman and M. Marcus, Existence and uniqueness results
for semilinear Dirchlet problems in annuli, Arch. Rational Meech. Anal., 108 (1989), 293-307.
[2] D. S. Cohen and H. B. Keller, Some positive problems suggested
by nonlinear heat equation, J. Math Mech., 16 (1967), 1361-1376.
[3] L. H. Erbe, Existence of solutions to boundary value problems
for second order differential equation, Nonlinear Analysis TM&A., 6 (1982), 1155-1162.
[4] L. H. Erbe, S. Hu and H. Wang, Multiple positive solutions of
boundary value problems, J. Math. Anal., 184 (1994), 743-748.
[5] L. H. Erbe and H. Wang, On the existence of positive solutions
of ordinary differential equations, Proc. Amer. Math. Soc., 120 (1994), 743-748.
[6] D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, (1988).
[7] G.. Iffland, Positive solutions of a problems of Emden-Fowler
type with a free boundary, SIANJ. Math. Anal., 18 (1987), 283-292.〔8] W. C. Lian, F. H. Wong and C. C. Yeh, On the existence of positive solutions of nonlinear Second order differential equations, Proc. Amer. Math. Soc., 124 (1996), 1117-1126.
[9] F. I. Njoku and F. Zanolin, Positive solutions for two-point BVP's: existence and multiplicity results, Nonlinear Analysis TM&A., 13 (1989), 1329-1333.
[10] J. Santanilla, Nonnegative solutions to boundary value problems for nonlinear first and second order ordinary differential
equations, J. Math. Anal. Appl., 126 (1987), 397-408.
[11] F. H. Wong, Existence of positive solutions for singular boundary value problems, Nonlinear Analysis TM&A., 21 (1993), 397-406.
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