Stability of delay differential equations with oscillating coefficients

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We study the solutions to the delay differential equation equation ẋ(t) = -a(t)x(t - h), where the coefficient a(t) is not necessarily positive. It is proved that this equation is exponentially stable provided that a(t) = b + c(t) for some positive constant b less than π(2h), and the integral ∫0t c(s)ds is sufficiently small for all t > 0. In this case the 3/2-stability theorem is improved.

Original languageEnglish
Pages (from-to)1-5
Number of pages5
JournalElectronic Journal of Differential Equations
StatePublished - 16 Aug 2010


  • Exponential stability
  • Linear delay differential equation


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