## Contributions to the Theory of Nonlinear Oscillations, Volume 1The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-20), Volume I, will be forthcoming. |

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### Contents

On System of Ordinary Differential Equations | 1 |

Oscillation of a Third Order Nonlinear Autonomous System | 39 |

Nonlinear DifferenceDifferential Equations | 89 |

Forced Oscillations in Nonlinear Systems | 149 |

Singular Perturbations of a Van der Pol Equation | 243 |

The Existence of Forced Periodic Solutions of Second Order Differential Equations near Certain Equilibrium Points of the Unforced Equation | 291 |

The Construction of Periodic Solutions of Singular Perturbation Problems | 313 |

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analytic apply approximation argument assume assumption base boundary bounded circuit closed complete condition connected consider constant contains continuous convergence corollary corresponding curve cycle defined definition degenerate depend derivatives determined differential equation direction exists fact Figure finite fixed point follows formal function given gives Hence holds hypothesis implies increasing independent initial integral interval least Lemma less lies limit linear Math means method negative nonlinear obtain obvious occur operator origin oscillations parameters particular path periodic solution plane positive problem Proof prove putting reduced region remain replace require respect result satisfies similar singular point stable sufficiently Suppose tends theorem theory trajectory transformation true uniformly unique unstable variables variational vector zero