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

Celik C., Develi F.

Periodica Mathematica Hungarica, 2021 (Journal Indexed in SCI Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1007/s10998-021-00400-2
  • Title of Journal : Periodica Mathematica Hungarica
  • Keywords: Progressive contractions, Hyperbolic partial differential equation, Hyers-Ulam stability, Fixed point theory, 1ST-ORDER, OPERATOR

Abstract

© 2021, Akadémiai Kiadó, Budapest, Hungary.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.