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Research Article | Open Access

Periodic problem for non-instantaneous impulsive partial differential equations

Huanhuan Zhang( ), Jia Mu
College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou, 730030, China
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Abstract

We obtain a new maximum principle of the periodic solutions when the corresponding impulsive equation is linear. If the nonlinear is quasi-monotonicity, we study the existence of the minimal and maximal periodic mild solutions for impulsive partial differential equations by using the perturbation method, the monotone iterative technique and the method of upper and lower solution. We give an example in last part to illustrate the main theorem.

Keywords

non-instantaneous impulsesevolution equationperiodic mild solutionthe monotone iterative techniqueexistence
CLC number: 34A37, 34B77, 47D06, 43K13

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 3345-3359
DOI: 10.3934/math.2022186

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Cite this article:
Zhang H, Mu J. Periodic problem for non-instantaneous impulsive partial differential equations. AIMS Mathematics, 2022, 7(3): 3345-3359. https://doi.org/10.3934/math.2022186

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Received: 05 September 2021
Accepted: 11 November 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)