maximal interval of existence of ordinary differential equations

Let $E\subset W$ where $W$ is a normed vector space, $f\in C^1(E)$ is a continuous differentiable map $f:E\to W$. Furthermore consider the ordinary differential equation

$$\dot{x}=f(x)$$

with the initial condition

$x(0)=x_0$.

For all $x_0\in E$ there exists a unique solution

$$x:I\to E$$

where $I=[-a,a]$, which also satify the initial condition of the initial value problem. Then there exists a maximal interval of existence $J=(\alpha ,\beta )$ such that $I\subset J$ and there exists a unique solution

$x:J\to E$.

Title	maximal interval of existence of ordinary differential equations
Canonical name	MaximalIntervalOfExistenceOfOrdinaryDifferentialEquations
Date of creation	2013-03-22 13:37:06
Last modified on	2013-03-22 13:37:06
Owner	Daume (40)
Last modified by	Daume (40)
Numerical id	8
Author	Daume (40)
Entry type	Theorem
Classification	msc 34A12
Classification	msc 35-00
Classification	msc 34-00