A note on blow-up solutions for a scalar differential equation with a discrete delay

Tetsuya Ishiwata, Yukihiko Nakata

研究成果: Article査読

抄録

We study blow-up solutions for a general scalar differential equation with a discrete delay. It is shown that the existence of blow-up solutions for a discrete delay differential equation (DDE) is proven by finding blow-up solutions to an associated autonomous ordinary differential equation (ODE). We give an example that the existence of blow-up solutions to an associated autonomous ODE does not necessarily imply the existence of blow-up solutions to DDEs. Nevertheless, for a class of discrete DDEs, we prove that the existence of blow-up solutions implies the existence of blow-up solutions to associated autonomous ODEs. For special cases, we study the asymptotic behavior and the blow-up rate of the blow-up solutions.

本文言語English
ジャーナルJapan Journal of Industrial and Applied Mathematics
DOI
出版ステータスAccepted/In press - 2022

ASJC Scopus subject areas

  • 工学(全般)
  • 応用数学

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