TY - JOUR
T1 - A note on blow-up solutions for a scalar differential equation with a discrete delay
AU - Ishiwata, Tetsuya
AU - Nakata, Yukihiko
N1 - Funding Information:
This work was supported by KAKENHI. No. 19H05599, No. 19K21836, No. 20K03734, No. 21H01001 and the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.
Publisher Copyright:
© 2022, The Author(s).
PY - 2022/12
Y1 - 2022/12
N2 - 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.
AB - 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.
KW - Blow-up solutions
KW - Delay differential equations
KW - Delay-induced blow-up
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U2 - 10.1007/s13160-022-00533-y
DO - 10.1007/s13160-022-00533-y
M3 - Article
AN - SCOPUS:85137242991
SN - 0916-7005
VL - 39
SP - 959
EP - 971
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
IS - 3
ER -