Analyticity of Solutions of Differential Equations with a Threshold Delay

  • Tibor KrisztinEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 94)


We consider the differential equation \(\dot{x}(t) = f(x(t),x(t - r))\) where the delay r = r(x(⋅ )) is defined by the threshold condition \(\int _{t-r}^{t}a(x(s),\dot{x}(s))\,\mathrm{d}s =\rho\) with a given ρ > 0. It is shown that if f and a are analytic functions and a is positive, then the globally defined bounded solutions are analytic.


Delay differential equation State-dependent delay Threshold condition Analyticity 



This paper is dedicated to the 70th birthday of István Győri. Supported by the Hungarian Scientific Research Fund Grant. No. K109782.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Bolyai Institute, MTA-SZTE Analysis and Stochastic Research GroupUniversity of SzegedSzegedHungary

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