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臺灣博碩士論文加值系統

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研究生:陳世傑
論文名稱:二階方程解的存在性
指導教授:王富祥
學位類別:碩士
校院名稱:國立台北師範學院
系所名稱:數理教育研究所
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:2004
畢業學年度:92
語文別:英文
論文頁數:9
中文關鍵詞:邊界值問題存在性
外文關鍵詞:Boundary value problemexistence
相關次數:
  • 被引用被引用:0
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在1989年, Gupta, Nieto and Sanchez [5] 已經證明下面的界值問題:{方程式詳見論文}
至少存在一個解。在本文裡,我們要將其成果推廣至如下的界值問題:
{方程式詳見論文}
也至少存在一個解。這裡 f 是一個有特定成長限制且連續的Caratheodory 函數。
In 1989, Gupta, Nieto and Sanchez [5] had proved the periodic problem {equation can be seen in paper}
has at least one solution. In this paper ,we attempt to the generalized periodic boundary value problem
{equation can be seen in paper}
has at least one solution, where f is a continuous and Caratheodory function which subject to some growth restrictions.
1.Introduction
2.Main Results
3.Reference
[1] J. Bebernes and Martelli, On the structure of the solution set for periodic boundary value problems, Nonlinear Anal. 4 (1980), 821-830.
[2] L. Cesari, Functional analysis, nonlinear differential equations and the alternative methods, Nonlinear Funtional Analysis and Differential Equations, Dekker New York (1976), 1-196.
[3] L. Cesari and R. Kannan, An abstract existence theorem at resonance, Proc. Amer. Math. Soc. 63 (1977), 211-225.
[4] L. Cesari and T. T. Bowman, Existence of solutions to nonself-adjoint boundary value problems for ordibary differential equations, Nonlinear Anal. 9 (1985), 1211-1225.
[5] C. P. Gupta , J. J. Nieto and L. Sanchez , Periodic solutions of some Lienard and Duffing equations, journal of mathematical analysis and applications 140 (1989) 67-82.
[6] C. P. Gupta, On functional equations of Fredholm and Hammerstein type with applications to existence of periodic solutions of certain ordinary differential equations, J. Intregral Equations 3 (1981), 21-41.
[7] C. P. Gupta and J. Mawhin, Asymptotic conditions at the two first eigenvalues for the periodic solutions of Lienard differential equations and inequality of E. Schmidt,
Z. Anal. Anwendungen 3 (1984), 33-42.
[8] J. P. Gossez, Some nonlinear differential equations with resonance at the first eigenvalue, Conf. Sem. Mat. Univ. Bari. 167 (1979)
[9] R. Kannan and B. Lakshmikanthan, Periodic solutions of nonlinear boundary value problems, Nonlinear Anal.6 (1982), 1-10.
[10] E. M. Landesman and A. C. Lazer, Nonlinear perturbations of a linear elliptic boundary value problem at resonance, J. Math. Mech. 19 (1970), 609-623.
[11] J. Manwhin and J. R. Ward, Nonuniform nonresonance conditions at the two first eigenvalues for periodic solutions of forced Lienard and Duffing equations, Rocky Mountain J. Math. 12 (1982). 643-654.
[12] J. Mawhin, Landesman-Lazer’s type problems for nonlinear equations, Conf. Sem. Math. Univ. Bari, 147 (1977).
[13] J. J. Nieto, Periodic solutions of nonlinear parabolic equations, J. Differential Equations 60 (1985), 90-102.
[14] J. J. Nieto and V. Hari Rao, Periodic solutions for scalar Lienard equations, Acta Math. Hung. 48 (1986), 59-66.
[15] S. Tersian, On the periodic problem for the equation , Funkcial. Ekvac. 28 (1985), 39-46.
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