# 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 MaximalIntervalOfExistenceOfOrdinaryDifferentialEquations 2013-03-22 13:37:06 2013-03-22 13:37:06 Daume (40) Daume (40) 8 Daume (40) Theorem msc 34A12 msc 35-00 msc 34-00