A note on blow-up solutions for a scalar differential equation with a discrete delay
In this note, blow-up solutions of delay differential equations (DDE) of the form \(\frac{dx}{dt} = F(x(t), x(t-1))\) are considered. It is proved that if there exists \(a\in\mathbb{R}\) such that the ordinary differential equation (ODE) \(\frac{dx}{dt} = F(x(t), a)\) has a blow-up solution, then the DDE has blow-up solutions. Conversely, it is also proved that, under certain conditions on \(F\), if the DDE has a blow-up solution, then there exists \(a\in\mathbb{R}\) such that the ODE has blow-up solutions. Various particular cases with examples are also provided to demonstrate the main results and remark points.
scientific article; zbMATH DE number 7625959
scientific article