数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1055-1063.

• 论文 • 上一篇    

上下解反向的脉冲微分包含解的存在性

罗艳, 谢文哲   

  1. 湖南科技大学数学与计算科学学院 湖南湘潭 411201
  • 收稿日期:2018-07-20 修回日期:2018-11-28 发布日期:2019-11-08
  • 通讯作者: 罗艳 E-mail:luoyan2527@126.com
  • 基金资助:
    湖南科技大学教学改革研究项目(907-G31714)

Existence of Solutions for Impulsive Differential Inclusions with Upper and Lower Solutions in the Reverse Order

Luo Yan, Xie Wenzhe   

  1. School of Mathematics and Computing Science, Hunan University of Science and Technology, Hunan Xiangtan 411201
  • Received:2018-07-20 Revised:2018-11-28 Published:2019-11-08
  • Supported by:
    Supported by the Teaching Reform Research Project of Hunan University of Science and Technology (907-G31714)

摘要: 该文讨论一阶脉冲微分包含非线性边界问题解的存在性.当下解α和上解β反向βα,通过使用Martelli不动点定理结合上下解方法建立存在性结果.同时,文中指出如果给出不同的上下解反向定义,也可以得到存在性结果.

关键词: 脉冲微分包含, 非线性边界条件, 不动点定理, 上下解反向

Abstract: In this paper, we discuss the existence of solutions for nonlinear boundary problem of first-order impulsive differential inclusions. In the presence of a lower solution α and an upper solution β in the reverse order βα, we establish the existence results by using Martelli's fixed point theorem with upper and lower solutions method. We find that if we give different definitions of lower and upper solutions in the reverse order, we can also get the existence results.

Key words: Impulsive differential inclusions, Nonlinear boundary conditions, Fixed point theorem, Lower and upper solutions in the reverse order

中图分类号: 

  • O175.1