东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2008, Vol. 29 ›› Issue (3): 433-436.DOI: -

• 论著 • 上一篇    下一篇

Banach空间二阶脉冲微分方程三点边值问题正解存在性

孙涛;杨静宇;段晓东;   

  1. 东北大学理学院;东北大学理学院;大连民族学院计算机学院 辽宁 沈阳 110004;辽宁 沈阳 110004;辽宁 大连 116600
  • 收稿日期:2013-06-22 修回日期:2013-06-22 出版日期:2008-03-15 发布日期:2013-06-22
  • 通讯作者: Sun, T.
  • 作者简介:-
  • 基金资助:
    国家自然科学基金(60573124)．

Existence of positive solution of three-point boundary value problems for second-order impulsive differential equation in banach space

Sun, Tao (1); Yang, Jing-Yu (1); Duan, Xiao-Dong (2)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110004, China; (2) School of Computer, Dalian Nationalities University, Dalian 116600, China
  • Received:2013-06-22 Revised:2013-06-22 Online:2008-03-15 Published:2013-06-22
  • Contact: Sun, T.
  • About author:-
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摘要： 关于非线性脉冲微分方程边值问题解、正解以及多个正解存在性的讨论在已有文献中涉及的方法有很多。包括上下解方法、不动点指数理论等.在Banach空间中利用严格集压缩算子范数形式的锥拉伸与锥压缩不动点定理讨论一类非线性脉冲微分方程三点边值问题的特殊情况,即η∈(t_m,1]正解和多个正解的存在性.并运用该定理考察了一个无穷维脉冲微分方程三点边值问题正解的存在性.

关键词: 二阶脉冲微分方程, 锥, 严格集压缩算子, 不动点, 正解

Abstract: There were many methods were used in other papers to discuss the existence of solutions, positive solutions and multiple positive solutions of boundary value problem for nonlinear impulsive differential equation, such as the method of upper and lower solution, fixed point index theory. The fixed point theorem of cone is used to study the existence of multiple positive solutions to three-point boundary value problem as a case in particular to the nonlinear impulsive equation, i.e., η Ε (tm, 1] in Banach space. And an example is given to show the application of main result.

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