# 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 |