Abstract
In this paper we investigate a class of impulsive wave equations. We prove existence of classical solutions for the considered class of equations. A new topological approach is applied to prove the existence of solutions. The arguments are based upon of a recent theoretical result. To the best of our knowledge, there is hardly any work dealing with such impulsive wave. The reason may be the complex arguments caused by impulsive perturbations.
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References
Brézis, H.: Periodic solutions of nonlinear vibrating strings and duality principles. Bull. Am. Math. So (N.S.) 8, 409–426 (1983)
Brézis, H., Coron, J.M., Nirenberg, L.: Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz. Commun. Pure Appl. Math. 33, 667–689 (1980)
Chang, K.C.: Solutions of asymptotically linear operator equations via Morse theory. Commun. Pure Appl. Math. 34, 693–712 (1981)
Chang, K.C., Wu, S.P., Li, S.J.: Multiple periodic solutions for an asymptotically linear wave equation. Indiana Univ. Math. J. 31(5), 721–731 (1982)
Polyanin, A., Manzhirov, A.: Hoandbook of Integral Equations. CRC Press, London (1998)
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Georgiev, S.G., Zennir, K. Existence of solutions for a class of nonlinear impulsive wave equations. Ricerche mat 71, 211–225 (2022). https://doi.org/10.1007/s11587-021-00649-2
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DOI: https://doi.org/10.1007/s11587-021-00649-2