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Research Article | Open Access

Existence of solutions for impulsive wave equations

Svetlin G. Georgiev1, Khaled Zennir2, Keltoum Bouhali2,4( ), Rabab alharbi2, Yousif Altayeb2, Mohamed Biomy2,3
Department of Differential Equations, Faculty of Mathematics and Informatics, University of Sofia, Sofia, Bulgaria
Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia
Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, 42511, Egypt
Departement de Mathématiques, Faculté des sciences, Université 20 Aôut 1955, Skikda, Algérie
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Abstract

We study a class of initial value problems for impulsive nonlinear wave equations. A new topological approach is applied to prove the existence of at least one and at least two nonnegative classical solutions. To prove our main results we give a suitable integral representation of the solutions of the considered problem. Then, we construct two operators so that any fixed point of their sum is a solution.

Keywords

wave equationsimpulsive wave equationspositive solutionfixed pointconesum of operators
CLC number: 35L05, 35R12, 55M20

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AIMS Mathematics
Volume 8 Issue 4,
April 2023
Pages 8731-8755
DOI: 10.3934/math.2023438

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Cite this article:
Georgiev SG, Zennir K, Bouhali K, et al. Existence of solutions for impulsive wave equations. AIMS Mathematics, 2023, 8(4): 8731-8755. https://doi.org/10.3934/math.2023438

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Received: 30 September 2022
Revised: 16 January 2023
Accepted: 25 January 2023
Published: 15 April 2023
©2023 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)