$ (\omega,\mathbb{T}) $-periodic solutions of impulsive evolution equations

Michal Fečkan; Kui Liu; JinRong Wang

doi:10.3934/eect.2021006

Article Contents

2022, Volume 11, Issue 2: 415-437. Doi: 10.3934/eect.2021006

This issue Previous Article An inverse problem for the pseudo-parabolic equation with p-Laplacian Next Article Analysis of nonlinear fractional diffusion equations with a Riemann-liouville derivative

$ (\omega,\mathbb{T}) $-periodic solutions of impulsive evolution equations

1.
Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina 842 48, Bratislava, Slovakia
2.
Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49,814 73 Bratislava, Slovakia
3.
Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, P. R. China
4.
College of Science, Guizhou Institute of Technology, Guiyang, Guizhou 550025, P. R. China
5.
School of Mathematical Sciences, Qufu Normal University, , Qufu, Shandong 273165, P. R. China

^* Corresponding author: JinRong Wang
^* Corresponding author: JinRong Wang

Received: August 31, 2020

Revised: October 31, 2020

Early access: January 2021

Published: April 2022

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Abstract

In this paper, we study $ (\omega,\mathbb{T}) $-periodic impulsive evolution equations via the operator semigroups theory in Banach spaces $ X $, where $ \mathbb{T}: X\rightarrow X $ is a linear isomorphism. Existence and uniqueness of $ (\omega,\mathbb{T}) $-periodic solutions results for linear and semilinear problems are obtained by Fredholm alternative theorem and fixed point theorems, which extend the related results for periodic impulsive differential equations.

Keywords:

Impulsive evolution equations,
$ (\omega \mathbb{T}) $-periodic solutions,
existence and uniqueness.

Mathematics Subject Classification: 34A37, 93B05, 93C25.

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References

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