1st Edition

Oscillation Theory for Functional Differential Equations

By Lynn Erbe, Q. Kong, B.G. Zhang Copyright 1995

    Examines developments in the oscillatory and nonoscillatory properties of solutions for functional differential equations, presenting basic oscillation theory as well as recent results. The book shows how to extend the techniques for boundary value problems of ordinary differential equations to those of functional differential equations.

    Preface

    Preliminaries

    Introduction

    Initial Value Problems

    Oscillation and Nonoscillation

    Formulation of Boundary Value Problems for Functional Differential Equations

    Fixed Point Theorems

    Oscillations of First Order Delay Differential Equations

    Introduction

    Stable Type Equations with a Single Delay

    The Distribution of Zeros of Oscillatory Solutions

    Unstable Type Equations

    Equations with Oscillatory Coefficients

    Equations with Positive and Negative Coefficients

    Equations with Several Delays

    Equations with Forced Terms

    Single Population Models with Delays

    Notes

    Oscillation of First Order Neutral Differential Equations

    Introduction

    Characteristic Equations

    Equations with Variable Coefficients (I)

    Equations with Variable Coefficients (II)

    Comparison Results

    Unstable Type Equations

    Sublinear Equations

    Equations with Mixed Coefficients

    Linearized Oscillation

    Equation with a Nonlinear Neutral Term

    Forced Equations

    Notes

    Oscillation and Nonoscillation of Second Order Differential Equations with Deviating Arguments

    Introduction

    Linearized Oscillation

    Existence of Oscillatory Solutions

    Strum Comparison Theorems

    Oscillation Criteria

    Classification of Nonoscillatory Solutions

    Unstable Type Equations

    Forced Oscillation

    Equations with a Nonlinear Neutral Term

    Advanced Type Equations

    Notes

    Oscillation of Higher Order Neutral Differential Equations

    Introduction

    Comparison Theorems for Odd Order Equations

    Oscillation and Nonoscillation of Odd Order Equations

    Oscillation of Even Order Equations

    Classification of Nonoscillatory Solutions

    Existence of Oscillatory Solutions

    Equations with Nonlinear Neutral Terms

    Unstable Type Equations

    Notes

    Oscillation of Systems of Neutral Differential Equations

    Introduction and Preliminaries

    Systems with Constant Matrix Coefficients

    Systems with Variable Matrix Coefficients

    Comparison with Scalar Equations

    Existence of Nonoscillatory Solutions

    Notes

    Boundary Value Problems for Second Order Functional Differential Equations

    Introduction

    Lipschitz Type Conditions

    Nagumo Type Condition

    Leray-Schauder Alternative

    Topological Transversality Method

    Boundary Value Problems for Singular Equations

    Notes

    References

    Index

    Biography

    Lynn Erbe