## Ordinary Differential Equations |

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### Contents

Preliminaries | 1 |

Existence | 8 |

Differential inequalities and uniqueness | 24 |

Copyright | |

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### Common terms and phrases

analogue analytic arbitrary assertion Assume assumption asymptotic Banach space bounded change of variables class C1 coefficients Consequently Consider const continuous exterior derivative continuous function convergent Corollary defined denote diag differential equations disconjugate egress point eigenvalues Exercise exists a constant exponential dichotomy exterior derivative fixed follows fundamental matrix given Hartman and Wintner Hence holds implies inequality initial conditions initial value problem integral interval of existence Jacobian Jacobian matrix Jordan curve Jordan normal form Lemma Let f(t linearly independent linearly independent solutions Lipschitz continuous Math nonsingular norm Note open set orbit periodic solution principal solution proof of Lemma proof of Theorem proves real-valued function Remark replaced respect result rj(t second order sequence Show solution of 1.1 solution satisfying solution u(t stationary point subset subspace Suppose Theorem 4.1 uniformly unique solution vector verified zeros