Hyers‐Ulam Stability of the Delay Equation y′(t) = λy(t − τ)

Soon-Mo Jung and Janusz Brzdęk

Abstract and Applied Analysis, 2010, vol. 2010, issue 1

Abstract: We investigate the approximate solutions y : [−τ, ∞) → ℝ of the delay differential equation y′(t) = λy(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.

Date: 2010
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https://doi.org/10.1155/2010/372176

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:372176

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