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

Celik, Canan; Develi, Faruk

doi:10.1007/s10998-021-00400-2

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

Celik C., Develi F.

PERIODICA MATHEMATICA HUNGARICA, cilt.84, sa.2, ss.211-220, 2022 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 84 Sayı: 2
Basım Tarihi: 2022
Doi Numarası: 10.1007/s10998-021-00400-2
Dergi Adı: PERIODICA MATHEMATICA HUNGARICA
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
Sayfa Sayıları: ss.211-220
Anahtar Kelimeler: Progressive contractions, Hyperbolic partial differential equation, Hyers-Ulam stability, Fixed point theory, 1ST-ORDER, OPERATOR
Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.