## Contributions to the Theory of Nonlinear OscillationsLamberto Cesari, Joseph P. LaSalle, Solomon Lefschetz The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-45), Volume V, will be forthcoming. |

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### Contents

The Time Optimal Control Problem | 1 |

Continuous Dependence on a Parameter | 25 |

Poincares Perturbation Method and Topological Degree | 37 |

On the Behavior of the Solutions of Linear Periodic | 55 |

On the Stability of Periodic Solutions of Weakly | 89 |

Existence Theorems for Periodic Solutions of Nonlinear | 115 |

The Applications of a Fixed Point Theorem to | 173 |

Quadratic Differential Equations and NonAssociative | 185 |

Sur Une Propriete De LEnsemble Des Trajectoires | 215 |

The Local Theory of Piecewise Continuous Differential | 225 |

Asymptotic Stability in 3Space | 257 |

Existence and Uniqueness of the Periodic Solution | 269 |

Appendix | 285 |

### Common terms and phrases

AC solutions algebra analytic functions assume asymptotically stable autonomous system bifurcation system bounded boundedness Cesari characteristic exponents characteristic roots compact components condition Consider the system constant contains continuous functions control system convex set Corollary corresponding curve defined deformation retract denote determining equations element equivalent existence theorems given hence homeomorphic idempotents implies integer isolated critical points J. K. Hale L-integrable Lemma linearly linearly equivalent linearly independent Math Mathieu equation mean value zero method of successive n-vector neighborhood nilpotent non-zero obtain optimal steering function ordinary differential equations parameter periodic coefficients periodic of period periodic solution PJ(O plane positive problem PROOF properties proved quadratic differential system real numbers related algebra replaced satisfied stability of periodic subset successive approximations sufficiently small suppose switching points switching space system of differential Theorem 3.1 theory topological degree trajectory weakly nonlinear