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

Celik C., Develi F.

PERIODICA MATHEMATICA HUNGARICA, vol.84, no.2, pp.211-220, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 84 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.1007/s10998-021-00400-2
  • Journal Name: PERIODICA MATHEMATICA HUNGARICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.211-220
  • Keywords: Progressive contractions, Hyperbolic partial differential equation, Hyers-Ulam stability, Fixed point theory, 1ST-ORDER, OPERATOR
  • Yıldız Technical University Affiliated: Yes

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.