Functional differential equation

Summary

A functional differential equation relates the derivative of an unknown function at time $t$ to its values at other times. Often these times fill a whole past interval. It includes ordinary differential equations, delay equations and equations with distributed memory. The state at time $t$ is the piece of the solution on an interval $[t - r, t]$, so the phase space is a space of functions. The theory, developed by Krasovskii, Hale and others, extends existence, uniqueness and stability theory to this setting.