非连续增算子的不动点定理及其应用
PDF下载 (423)李冰冰,吴献超.非连续增算子的不动点定理及其应用[J].宁波大学学报(理工版),2013,26(01):63-68.DOI:
LI Bing-bing,WU Xian-chao.Fixed Point Theorems for Discontinuous Increasing Operators and Applications[J].Journal of Ningbo University(Natural Science & Engineering Edition),2013,26(01):63-68.DOI:
| Title: | Fixed Point Theorems for Discontinuous Increasing Operators and Applications |
| 作者: | 李冰冰, 吴献超 |
| Author(s): | LI Bing-bing, WU Xian-chao |
| 关键词: | 增算子; 不动点; 含间断项的脉冲积－微分方程; 初值问题 |
| Keywords: | increasing operators; fixed points; discontinuous impulsive integro-differential equation; initial value problem |
| 分类号: | O17 |
| 文献标识码: | A |
| 摘要: | 给出了Banach空间的一个增算子不动点定理, 将这一定理应用到Banach空间含间断项的二阶非线性脉冲积－微分方程, 给出了一类方程的最大解和最小解的存在性定理. 应用以上2个定理并通过建立比较定理, 讨论了Banach空间含间断项的二阶非线性脉冲积－微分方程的初值问题的最大解、最小解的存在性, 并且在应用定理时仅用锥正规, 减弱了刘笑颖等提出的锥正则条件. |
| Abstract: | In this paper, a new fixed point theorem for discontinuous increasing operator in Banach Spaces is derived. The theorem is applied to the second order discontinuous nonlinear impulsive integro-differential equations in Banach spaces, and the result about the existence of its maximal and minimal solutions is obtained. The initial value problems for second order discontinuous nonlinear impulsive integro-differential equations in Banach spaces are investigated. By establishing comparison theorems and using a fixed point theorem, the existence of maximal and minimal solutions is proved. The findings in this paper generalize and improve the relevant results presented in some well-known prestigious literatures. |
| 参考文献 /References: | [1] 张金清, 孙经先. 一个非连续增算子不动点定理及其应用[J]. 应用数学学报, 2001, 24(1):34-43. [2] 刘笑颖, 吴从炘. Banach空间不连续的脉冲微分－积分方程的解与迭代解[J]. 数学学报, 2001, 44(3):469- 474. [3] 刘笑颖, 吴从炘. 非连续弱紧增算子的不动点及其对Banach空间初值问题的应用[J]. 系统科学与数学, 2000, 20(2):175-180. [4] 孙经先. 非连续的增算子的不动点定理及其对含间断项的非线性方程的应用[J]. 数学学报, 1988, 31(1): 101-107. [5] 刘笑颖, 吴从炘. Banach空间不连续的脉冲微分－积分方程的周期边值问题[J]. 系统科学与数学, 2003, 23(3):374-380. [6] 张金清. 增算子的不动点定理及其对含间断项非线性脉冲方程的应用[J]. 数学学报, 2002, 45(6):1087-1098. [7] 孙经先. 非线性泛函分析序集一般原理的推广[J]. 系统科学与数学, 1990, 10(3):228-232. [8] 夏道行, 舒五昌, 严绍宗, 等. 泛函分析第二教程[M]. 北京: 高等教育出版社, 1987:42. [9] 孙经先. 增算子的不动点定理及其对Banach空间含间断项的非线性方程的应用[J]. 数学学报, 1991, 34(5): 665-674. [10] Liu Xinzhi, Guo Dajun. Periodic Boundary value problems for a class of second order impulsive integro-differential equations in Banach spaces[J]. Math Appl, 1997, 216(1):284-302. [11] Guo Dajun. Initial value problem for nonlinear second order impulsive integro-differential equations in Banach spaces[J]. Math Anal Appl, 1996, 200(1):1-13. |
| 备注/Memo: | 收稿日期: 2012?01?10. 第一作者: 李冰冰（1983－）, 女, 辽宁鞍山人, 硕士/讲师, 主要研究方向: 非线性泛函分析. E-mail: qiwu_feiyang@163.com 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
