The method of lower and upper solutions for impulsive fractional evolution equations in Banach spaces
J. Korean Math. Soc. 2020 Vol. 57, No. 1, 61-88
https://doi.org/10.4134/JKMS.j180526
Published online January 1, 2020
Haide Gou, Yongxiang Li
Northwest Normal University; Northwest Normal University
Abstract : 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
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