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J. Korean Math. Soc. 2020; 57(1): 61-88

Online first article October 17, 2019      Printed January 1, 2020

https://doi.org/10.4134/JKMS.j180526

Copyright © The Korean Mathematical Society.

The method of lower and upper solutions for impulsive fractional evolution equations in Banach spaces

Haide Gou, Yongxiang Li

Northwest Normal University; Northwest Normal University

Abstract

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In this paper, we investigate the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition by means of the method of upper and lower solutions and monotone iterative method. Using the theory of Kuratowski measure of noncompactness, a series of results about mild solutions are obtained. Finally, two examples are given to illustrate our results.

Keywords: Upper and lower solution, impulsive fractional evolution equation, monotone iterative technique, $C_0$-semigroup

MSC numbers: 26A33, 34K30, 34K45, 35G10, 47D06

Supported by: This work was nancially supported by the National Natural Science Foundation of China(Grant No.11661071).

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