A kind of stricter Hyers-Ulam stability of second order linear differential equations of Carathéodory type
type: Item
instance of: scholarly article
title: A kind of stricter Hyers-Ulam stability of second order linear differential equations of Carathéodory type
zbMATH Open document ID: 1471.34030
author: Yanyan Li
published in: Applied Mathematics Letters
publication date: 2021-03-04T00:00:00Z
review text: In this work, the authors study Hyers-Ulam stability conditions for second order linear differential equations \[ \phi'' + b_1 \phi' + b_0 \phi = f(t), \quad t\in (\sigma, \tau) \tag{1} \] \((-\infty \le\sigma < \tau \le +\infty),\) where \(f(t)\) is a real-valued locally integrable function on \((\sigma,\tau)\), \(b_1, b_0 \in \mathbb{R}\). Let \(\lambda_1, \lambda_2\) be the characteristic numbers of the corresponding homogeneous equation \[ \phi'' + b_1 \phi' + b_0 \phi = 0, \quad t\in (\sigma, \tau). \tag{1} \] The main result of this work (Theorem 1) states that if under some restrictions on \(\lambda_1\) and \(\lambda_2\) Eq. (1) has a Hyers-Ulam stricter \(\widetilde{\phi}(t)\) (in some sense an approximate solution to Eq. (1); see Definition 2) then Eq. (1) has an exact (Carateodory) solution \(\phi(t)\) close to \(\widetilde{\phi}(t)\) on \((\sigma, \tau)\) by sup-norm: \(\sup\limits_{t\in (\sigma, \tau)} |\phi(t) - \widetilde{\phi}(t)| \le \varepsilon\), for every \(\varepsilon >0\), corresponding to the Hyers-Ulam stricter \(\widetilde{\phi}(t)\).
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34D10
zbMATH DE Number: 7317515
zbMATH Keywords: stricter Hyers-Ulam stability
zbMATH Keywords: linear differential equation
zbMATH Keywords: Carathéodory type
Wikidata QID: Q115360735
reviewed by: G. A. Grigorian
MaRDI profile type: Publication
full work available at URL: j.aml.2020.106946
OpenAlex ID: W3112162638
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DOI: 10.1016/J.AML.2020.106946
description: scientific article; zbMATH DE number 7317515