1st Edition
Oscillation Theory for Functional Differential Equations
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