JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (6): 57-67.doi: 10.6040/j.issn.1671-9352.0.2022.595

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Existence of mild solutions for the nonlocal problem of second-order impulsive evolution equations

Li LI(),He YANG*()   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2022-11-14 Online:2023-06-20 Published:2023-05-23
  • Contact: He YANG E-mail:2430353979@qq.com;yanghe@nwnu.edu.cn

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Abstract:

A new definition of mild solutions of the second-order impulsive evolution equations involving nonlocal condition $ u(0)=\sum\limits_{k=1}^n C_k u\left(\tau_k\right)$ is given by introducing a Green function. Then, the existence of mild solutions of the concerned problem is proved by applying the Sadovskii fixed point theorem. At last, an example is provided as an application of the obtained abstract result.

Key words: second-order impulsive evolution equation, cosine family, nonlocal condition, Sadovskii fixed point theorem, mild solution

CLC Number: 

  • O175.15
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