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

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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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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  • DOI: https://doi.org/10.1007/s10998-021-00400-2

Keywords

  • Progressive contractions
  • Hyperbolic partial differential equation
  • Hyers–Ulam stability
  • Fixed point theory

Mathematics Subject Classification

  • 35L70
  • 39B82
  • 47H10