# Growth Rates of Solutions of Superlinear Ordinary Differential Equations

## TL;DR

This paper derives precise growth rate estimates for solutions of superlinear nonlinear ordinary differential equations with nonautonomous forcing, highlighting their rapid growth and finite-time blow-up, which are crucial for understanding complex dynamical systems.

## Contribution

It provides sharp estimates on the growth rates of solutions to a class of superlinear ODEs with nonautonomous forcing, advancing understanding of their asymptotic behavior.

## Key findings

- Solutions exhibit rapid growth and finite-time blow-up.
- Sharp estimates on the solutions' growth rates are established.
- The results are relevant for complex systems with delay and randomness.

## Abstract

In this letter we obtain sharp estimates on the growth rate of solutions to a nonlinear ODE with a nonautonomous forcing term. The equation is superlinear in the state variable and hence solutions exhibit rapid growth and finite-time blow-up. The importance of ODEs of the type considered here stems from the key role they play in understanding the asymptotic behaviour of more complex systems involving delay and randomness.