Monotone Iterative Technique for $S$-Asymptotically Periodic Problem of Evolution Equation with Delay

Monotone Iterative Technique for $S$-Asymptotically Periodic Problem of Evolution Equation with Delay

Year:    2022

Author:    Qiang Li, Hong Qiao

Journal of Mathematical Study, Vol. 55 (2022), Iss. 4 : pp. 381–397

Abstract

This paper is concerned with $S$-asymptotically periodic problem of evolution equation with delay in ordered Banach space. Under some weaker assumptions, we construct monotone iterative method in the presence of the lower and upper solutions to the delayed evolution equation, and obtain the existence of maximal and minimal $S$-asymptotically periodic mild solutions. Finally, we give an example to exhibit the practicability of our abstract results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v55n4.22.03

Journal of Mathematical Study, Vol. 55 (2022), Iss. 4 : pp. 381–397

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Evolution equation delay $S$-asymptotically periodic mild solutions monotone iterative technique positive C$_0$-semigroup.

Author Details

Qiang Li

Hong Qiao