Existence of positive S-asymptotically periodic solutions of the fractional evolution equations in ordered Banach spaces
Articles
Qiang Li
Qufu Normal University
https://orcid.org/0000-0001-5380-7420
Lishan Liu
Qufu Normal University
https://orcid.org/0000-0001-8541-1017
Mei Wei
Northwest Normal University
https://orcid.org/0000-0003-0140-4237
Published 2021-09-01
https://doi.org/10.15388/namc.2021.26.24176
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Keywords

fractional evolution equation
S-asymptotically periodic solution
positive C0-semigroup
positive mild solution
monotone iterative method

How to Cite

Li Q., Liu L. and Wei M. (2021) “Existence of positive S-asymptotically periodic solutions of the fractional evolution equations in ordered Banach spaces”, Nonlinear Analysis: Modelling and Control, 26(5), pp. 928-946. doi: 10.15388/namc.2021.26.24176.

Abstract

In this paper, we discuss the asymptotically periodic problem for the abstract fractional evolution equation under order conditions and growth conditions. Without assuming the existence of upper and lower solutions, some new results on the existence of the positive S-asymptotically ω-periodic mild solutions are obtained by using monotone iterative method and fixed point theorem. It is worth noting that Lipschitz condition is no longer needed, which makes our results more widely applicable.

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