Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations

Marian, Daniela

doi:10.3390/math9243260

Open AccessArticle

Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations

by

Daniela Marian

Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania

Mathematics 2021, 9(24), 3260; https://doi.org/10.3390/math9243260

Submission received: 11 November 2021 / Revised: 9 December 2021 / Accepted: 14 December 2021 / Published: 15 December 2021

(This article belongs to the Special Issue Advances in Delay Differential Equations)

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Abstract

In this paper, we study semi-Hyers–Ulam–Rassias stability and generalized semi-Hyers–Ulam–Rassias stability of differential equations

x^{'} (t) + x (t - 1) = f (t)

and

x^{″} (t) + x^{'} (t - 1) = f (t), x (t) = 0 if t \leq 0,

using the Laplace transform. Our results complete those obtained by S. M. Jung and J. Brzdek for the equation

x^{'} (t) + x (t - 1) = 0

.

Keywords: semi-Hyers–Ulam–Rassias stability; delay differential equations; Laplace transform

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MDPI and ACS Style

Marian, D. Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations. Mathematics 2021, 9, 3260. https://doi.org/10.3390/math9243260

AMA Style

Marian D. Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations. Mathematics. 2021; 9(24):3260. https://doi.org/10.3390/math9243260

Chicago/Turabian Style

Marian, Daniela. 2021. "Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations" Mathematics 9, no. 24: 3260. https://doi.org/10.3390/math9243260

APA Style

Marian, D. (2021). Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations. Mathematics, 9(24), 3260. https://doi.org/10.3390/math9243260

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations

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