Existence of solutions for impulsive wave equations

Svetlin G. Georgiev; Khaled Zennir; Keltoum Bouhali; Rabab alharbi; Yousif Altayeb; Mohamed Biomy; Svetlin G. Georgiev; Khaled Zennir; Keltoum Bouhali; Rabab alharbi; Yousif Altayeb; Mohamed Biomy

doi:10.3934/math.2023438

AIMS Mathematics

2023, Volume 8, Issue 4: 8731-8755. doi: 10.3934/math.2023438

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Existence of solutions for impulsive wave equations

1.
Department of Differential Equations, Faculty of Mathematics and Informatics, University of Sofia, Sofia, Bulgaria
2.
Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia
3.
Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, 42511, Egypt
4.
Departement de Mathématiques, Faculté des sciences, Université 20 Aôut 1955, Skikda, Algérie

Received: 30 September 2022 Revised: 16 January 2023 Accepted: 25 January 2023 Published: 07 February 2023
MSC : 35L05, 35R12, 55M20

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.
- wave equations,
- impulsive wave equations,
- positive solution,
- fixed point,
- cone,
- sum of operators
Citation: Svetlin G. Georgiev, Khaled Zennir, Keltoum Bouhali, Rabab alharbi, Yousif Altayeb, Mohamed Biomy. Existence of solutions for impulsive wave equations[J]. AIMS Mathematics, 2023, 8(4): 8731-8755. doi: 10.3934/math.2023438

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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.

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