## Oscillation and Dynamics in Delay Equations: Proceedings of an AMS Special Session Held January 16-19, 1991Oscillation theory and dynamical systems have long been rich and active areas of research. Containing frontier contributions by some of the leaders in the field, this book brings together papers based on presentations at the AMS meeting in San Francisco in January, 1991. With special emphasis on delay equations, the papers cover a broad range of topics in ordinary, partial, and difference equations and include applications to problems in commodity prices, biological modeling, and number theory. The book would be of interest to graduate students and researchers in mathematics or those in other fields who have an interest in delay equations and their applications. |

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### Contents

1 | |

A Wave Equation Viewed as an Ordinary Differential Equation | 23 |

The Oscillation and Exponential Decay Rate of Solutions of Differential Delay Equations | 43 |

Transition Layers for a Singularly Perturbed 2Dimensional System of DifferentialDifference Equations | 55 |

Differential Difference Equations in Analytic Number Theory | 73 |

A Simple Model for Price Fluctuations in a Single Commodity Market | 97 |

Some Results on the Asymptotic Behavior of the Solutions of a Second Order Nonlinear Neutral Delay Equation | 105 |

Linearized Oscillations for Nonautonomous Delay Difference Equations | 115 |

Small Solutions and Completeness for Linear Functional Differential Equations | 127 |

Periodic Solutions of Differential Delay Equations with ThresholdType Delays | 153 |

Unstable Manifolds of Periodic Orbits of a Differential Delay Equation | 177 |

The Fourier Method for Partial Differential Equations with Piecewise Continuous Delay | 241 |

### Other editions - View all

Oscillation and Dynamics in Delay Equations: Proceedings of an AMS Special ... John R. Graef,Jack K. Hale No preview available - 1992 |

Oscillation and Dynamics in Delay Equations: Proceedings of an AMS Special ... John R. Graef,Jack K. Hale No preview available - 1992 |

### Common terms and phrases

Anal argument assume Banach space bounded characteristic matrix Class I4 closed curves Consider constant continuous contradiction Corollary defined delay differential equations denote difference equations differential delay equations E(det eigenfunctions eigenvalues entire function estimate eventually positive exists exponential decay exponential type ext(p o Floquet Floquet multiplier follows functional differential equations given Hence heteroclinic orbit holds implies inequality int(p o m integer interval Ladas Lemma Lipschitz Lyapunov function M. K. Grammatikopoulos Math Mathematics Subject Classification Necessary and sufficient neutral differential equations nonlinear nonoscillatory solution Number Theory obtain oscillating periodic solution oscillatory periodic solutions phase curve positive solution Proposition real roots satisfies Section semigroup sequence sieve slowly oscillating periodic slowly oscillating solutions small solutions solution of eq solution y(t sufficient conditions Suppose Theorem 5.1 unbounded unstable Y. G. Sficas yields zero