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February 2022 Periodic solutions of impulsive differential equations with piecewise alternately advanced and retarded argument of generalized type
Kuo-Shou Chiu
Rocky Mountain J. Math. 52(1): 87-103 (February 2022). DOI: 10.1216/rmj.2022.52.87

Abstract

We investigate the existence of the periodic solutions of a quasilinear impulsive differential equation with alternately advanced and retarded arguments of generalized type, in short IDEPCAG. By using some fixed point theorems and some new analysis techniques, sufficient conditions are obtained for the existence and uniqueness of periodic solutions of these IDEPCAG systems. A new IDEPCAG’s Gronwall-type lemma is proved. Some examples concerning impulsive biological models such as Lasota–Ważewska model, Nicholson’s blowflies and logistic models are treated.

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Kuo-Shou Chiu. "Periodic solutions of impulsive differential equations with piecewise alternately advanced and retarded argument of generalized type." Rocky Mountain J. Math. 52 (1) 87 - 103, February 2022. https://doi.org/10.1216/rmj.2022.52.87

Information

Received: 15 February 2021; Revised: 31 March 2021; Accepted: 2 April 2021; Published: February 2022
First available in Project Euclid: 19 April 2022

Digital Object Identifier: 10.1216/rmj.2022.52.87

Subjects:
Primary: 34A37 , 34K13
Secondary: 26D10 , 34A36 , 37C25

Keywords: ‎fixed point theorems , Gronwall’s inequality , Impulsive differential equation , periodic solutions , Piecewise constant argument of generalized type

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 1 • February 2022
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