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

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Listed:
  • Soon-Mo Jung
  • Janusz Brzdęk

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.

Suggested Citation

  • Soon-Mo Jung & Janusz Brzdęk, 2010. "Hyers‐Ulam Stability of the Delay Equation y′(t) = λy(t − τ)," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    • Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:372176
    DOI: 10.1155/2010/372176
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    References listed on IDEAS

    as
    1. Yongjin Li & Yan Shen, 2009. "Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-7, October.
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