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Existence and Hyers–Ulam stability of solutions for a delayed hyperbolic partial differential equation

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Abstract

In this paper, we first prove the existence and uniqueness of the solutions for a delayed hyperbolic partial differential equation by applying the progressive contraction technique introduced by Burton (Nonlinear Dyn Syst Theory 16(4): 366–371, 2016; Fixed Point Theory 20(1): 107–113, 2019) to the corresponding fixed-point problem. Then we derive a Hyers–Ulam stability result for this differential equation by using a Wendorff-type inequality and the Abstract Gronwall Lemma.

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Authors and Affiliations

  1. Department of Mathematics, Yildiz Technical University, Istanbul, Turkey

    Canan Çelik & Faruk Develi

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  1. Canan Çelik
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  2. Faruk Develi
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Correspondence to Faruk Develi.

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Çelik, C., Develi, F. Existence and Hyers–Ulam stability of solutions for a delayed hyperbolic partial differential equation. Period Math Hung 84, 211–220 (2022). https://doi.org/10.1007/s10998-021-00400-2

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