## Uniqueness and Nonuniqueness Criteria for Ordinary Differential EquationsThis monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions. |

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### Contents

Section 1 | 1 |

Section 2 | 55 |

Section 3 | 83 |

Section 4 | 86 |

Section 5 | 102 |

Section 6 | 108 |

Section 7 | 128 |

Section 8 | 134 |

Section 11 | 208 |

Section 12 | 210 |

Section 13 | 225 |

Section 14 | 248 |

Section 15 | 251 |

Section 16 | 263 |

Section 17 | 272 |

Section 18 | 282 |

Section 9 | 175 |

Section 10 | 204 |

Section 19 | 295 |

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### Common terms and phrases

absolutely continuous Banach space classical abstract solution conditions of Theorem Consider the initial constant continuous and nonnegative continuous for x0 continuous function continuous in S+ continuously differentiable contradiction Corollary defined and continuous differential inequality Example exists a Lyapunov extended solution finite following result function f(x,y function y(x Further hence Henstock integral hypothesis implies initial value problem interval x0 Lebesgue Lebesgue integrable Lemma Let f(x,y Let the function Let y(x limsup Lipschitz condition 1.2.1 Lipschitz Uniqueness Theorem Lyapunov function Lyapunov function V(x,y Math maximal solution mean value theorem nondecreasing nonincreasing ordinary differential equations positive number proof of Theorem satisfies the conditions satisfies the inequality satisfies the Lipschitz sequence solution in 0,a solutions of 1.1.1 sufficiently small Suppose that y(x Suppose y(x unique solution value problem 1.1.1 XQ,XO XQ,XQ y(xi y(Xo zero

### Popular passages

Page 309 - Conditions for the existence and uniqueness of a solution of the Cauchy problem for a system of ordinary differential equations with hysteresis nonlinearities', Dokl.

Page 308 - On a mean-value theorem of the differential calculus of vector -valued functions, and uniqueness theorems for ordinary differential equations in a linear normed space, in: Contributions to Differential Equations, Vol.