Abstract and Applied Analysis

Hyers-Ulam Stability of the Delay Equation y ' ( t ) = λ y ( t - τ )

Soon-Mo Jung and Janusz Brzdęk

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Abstract

We investigate the approximate solutions y : [ - τ , ) of the delay differential equation y ' ( t ) = λ y ( t - τ ) ( t [ 0 , ) ) with an initial condition, where λ > 0 and τ > 0 are real constants. We show that they can be “approximated” by solutions of the equation that are constant on the interval [ - τ , 0 ] and, therefore, have quite simple forms. Our results correspond to the notion of stability introduced by Ulam and Hyers.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 372176, 10 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313170931

Digital Object Identifier
doi:10.1155/2010/372176

Mathematical Reviews number (MathSciNet)
MR2746009

Zentralblatt MATH identifier
1210.34108

Citation

Jung, Soon-Mo; Brzdęk, Janusz. Hyers-Ulam Stability of the Delay Equation $y'(t)=\lambda y(t-\tau)$. Abstr. Appl. Anal. 2010 (2010), Article ID 372176, 10 pages. doi:10.1155/2010/372176. https://projecteuclid.org/euclid.aaa/1313170931


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