## Nonlinear differential equations |

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### Contents

PRELIMINARY CONSIDERATIONS | 1 |

THE EXISTENCE AND THE UNIQUENESS OF A SOLUTION | 41 |

PROPERTIES OF SOLUTIONS | 60 |

Copyright | |

6 other sections not shown

### Common terms and phrases

analytic asymptotically stable axis bounded Chap characteristic multiplier characteristic numbers coefficients Consider constant matrix continuously differentiable converges corresponding cosh critical points define derivative differential equation direction field Discuss Duffing equation dx/dt equation d2x/dt2 equivalent Example Exercise exists Explain expressed Gronwall's lemma Hence implies impressed frequency inequality initial condition initial values initial vector initial-value problem Jacobian Jordan curve Liapunov Liapunov function limit cycle linear approximation linear system linear transformation Mathieu equation nonlinearity condition nonsingular nonsingular matrix nontrivial normal solution obtain orbital stability origin parameter periodic matrix periodic orbit periodic solution plane positive limit cycle possesses a periodic principal matrix solution proof of Theorem resonance result right-hand member root saddle point satisfies scalar second-order equation singular point singular solution solution of period solution x(t sufficiently small tion uniformly unique vanish variable variational equations vector equation zero