## Lectures on ordinary differential equations |

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### Contents

Preliminaries | 3 |

Existence and Uniqueness Theorems | 25 |

Appendix A Some Differential Equations of FunctionTheoretical | 63 |

Copyright | |

13 other sections not shown

### Common terms and phrases

absolutely convergent algebra analytic analytic functions argument assume assumption asymptotic B-algebra boundary value problem branch-points characteristic values coefficients complex number consider constant continuous corresponding curve defined derivative determine discussion disk domain element of 93 entire function estimate exists finite number fixed follows formula given gives half-plane Hence holds holomorphic holomorphic function idempotent identity implies indicial equation inequality infinity initial values integral interval left member Lemma limit linearly independent mapping Math matrix meromorphic function multiple norm obtain oscillatory parameter polynomial positive numbers power series properties prove real axis regular singular point respect result Riccati equation right member roots satisfies second order Section sequence Show simple pole solution w(z space spectral spectrum subdominant subdominant solution Suppose theory transformation uniform convergence uniformly unique solution upper half-plane vector Verify zeros and extrema