Author:
Ishiwata Tetsuya,Nakata Yukihiko
Abstract
AbstractWe 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Engineering
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