Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (5): 1055-1063.

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

Yan Luo*(),Wenzhe Xie   

  1. School of Mathematics and Computing Science, Hunan University of Science and Technology, Hunan Xiangtan 411201
  • Received:2018-07-20 Online:2019-10-26 Published:2019-11-08
  • Contact: Yan Luo
  • Supported by:
    the Teaching Reform Research Project of Hunan University of Science and Technology(907-G31714)


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

CLC Number: 

  • O175.1