一阶混合型积分微分方程的周期边值问题

Periodic Boundary Value Problems for First Order Integrodifferential Equations of Mixed Type

Department of Mathematics, Xuzhou Normal University, Xuzhou, Jiangsu 221009, P R China

摘要: 在有一般化的上下解的条件下,研究了一阶混合型积分微分方程的周期边值问题的可解性和最小最大解的存在性。讨论基于迭合度方法,单调迭代方法和新的比较定理。
- 一般化的上下解 /
- 迭合度 /
- 单调迭代 /
- 混合型积分微分方程
Abstract: The existence of at least one solution and the existence of extreme solutions of periodic boundary value problems for first order integrodifferential equations of mixed type are studied,in the presence of generalized upper and lower solutions. The discussion is based on new comparative theorems and coincidence degree and monotone iterative methods.
- generalized upper and lower solutions /
- coincidence degree /
- monotone iteration /
- integrodifferential equation of mixed type

[1]	Ladde G S, Lakshmikantham V, Vatsala.Monotone Iterative Techniques of Nonlinear Differential
[2]	Equations[M].Boston:Pitman Publishing Inc,1985.
[3]	Kaul S K, Vatsla A S.Monotone method for integrodifferential equations with periodic boundary conditions[J].Appl Anal,1986,21(4):297～305.
[4]	Hu Shouchuan, Lakshmikantham V.Periodic boundary value problems for integrodifferential equations of Volterra type[J].Nonlinear Anal,1986,10(11):1203～1208.
[5]	Cabada A.The monotone method for first-order problems with linear and nonlinear boundary conditins[J].Appl Math Comp,1994,151(1):163～186.
[6]	Cheng Yubo, Zhuang Wan.On monotone iterative method for periodic boundary value problems of nonlinear integrodifferential equations[J].Nonlinear Anal,1994,22(3):295～303.
[7]	Nkashama M N.A generalization upper and lower solutions methods and multiplicity results for nonlinear first-order ODEs[J].J Math Anal Appl,1998,140(2):381～395.
[8]	Erbe L H, Guo Dajun.Periodic boundary value problems for second order integrodifferential equations of mixed type[J].Anal Appl,1992,46(4):249～258.
[9]	盖尔鲍姆,奥姆斯特德.分析中的反例[M](高枚译).上海:上海科学技术出版社,1980.
[10]	Gaines R E, Mawhin J L.Coincidence Degree and Nonlinear Differential Equations[M].Lecture Notes in Math,Vol.568,Berlin,New York:Springer-Verlag,1977.