@article{Georgiev2023, 
author = {Svetlin G. Georgiev and Khaled Zennir and Keltoum Bouhali and Rabab alharbi and Yousif Altayeb and Mohamed Biomy},
title = {Existence of solutions for impulsive wave equations},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {4},
pages = {8731-8755},
keywords = {wave equations, impulsive wave equations, positive solution, fixed point, cone, sum of operators},
url = {https://www.sciopen.com/article/10.3934/math.2023438},
doi = {10.3934/math.2023438},
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.}
}