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Nonoscillation and Oscillation:

Theory for Functional Differential Equations by Ravi P. Agarwal, Martin Bohner, Wan-Tong Li

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** Nonoscillation and Oscillation: Theory for Functional Differential Equations ** written by
** Ravi P. Agarwal **, Florida Institute of Technology, Melbourne, Florida,
** Martin Bohner**, University of Missouri, Rolla, Missouri and
** Wan-Tong Li **, Lanzhou University, China.

This book is devoted to a rapidly developing branch of the qualitative theory of differential equations with or without delays. It summarizes the most recent contributions of the authors and their colleagues in this area and will be a stimulus to its further development.

This book is addressed to a wide audience of specialists such as mathematicians, physicists, engineers and biologists. It can be used as a textbook at the graduate level and as a reference book for several disciplines.

** Nonoscillation and Oscillation: Theory for Functional Differential Equations ** written by
** Ravi P. Agarwal, Martin Bohner, Wan-Tong Li **
cover the following topics.

1.1. Introduction

1.2. Initial Value Problems

1.3. Definition of Oscillation

1.4. Some Fixed Point Theorems

1.5. Notes

2.1. Introduction

2.2. Equations with a Single Delay: General Case

2.3. Equations with Variable Delay: Critical Case

2.4. Equations with Constant Delay

2.5. Equations with Several Delays

2.6. Equations with Piecewise Constant Argument

2.7. Notes

3.1. Introduction

3.2. Comparison Theorems and Oscillation

3.3. Oscillation of Equations with Variable Coefficients (I)

3.4. Oscillation of Equations with Variable Coefficients (II)

3.5. Existence of Nonoscillating Solutions

3.6. Classification Schemes of Positive Solutions

3.7. Positive Solutions of Neutral Perturbed Equations

3.8. Notes

4.1. Introduction

4.2. Oscillation of Superlinear Equations

4.3. Oscillation of Sublinear Equations

4.4. Oscillation of Nonlinear Equations

4.5. Forced Oscillation of Nonlinear Equations

4.6. Positive Solutions of Nonlinear Equations

4.7. Oscillation of Half-Linear Equations

4.8. Notes

5.1. Introduction

5.2. Nonoscillation of Half-Linear Equations

5.3. Classification Schemes for Iterative Equations

5.4. Nonoscillation of Nonlinear Equations with 8 ds/r(s) < 8

5.5. Nonoscillation of Nonlinear Equations with 8 ds/r(s) = 8

5.6. Notes

6.1. Introduction

6.2. Comparison Theorems and Oscillation

6.3. Oscillation Criteria for Neutral Equations

6.4. Asymptotic Behavior of Nonoscillatory Solutions

6.5. Positive Solutions of Nonlinear Equations

6.6. Classifications of Nonoscillatory Solutions

6.7. Asymptotic Trichotomy for Positive Solutions

6.8. Existence of Nonoscillatory Solutions

6.9. Notes

7.1. Introduction

7.2. Oscillation of Nonlinear Systems

7.3. Oscillation of Nonlinear Systems with Forcing

7.4. Classification Schemes of Positive Solutions (I)

7.5. Classification Schemes of Positive Solutions (II)

7.6. Positive Solutions of Second Order Systems

7.7. Nonoscillation of Emden–Fowler Systems

7.8. Notes

8.1. Introduction

8.2. The Time Scales Calculus

8.3. Oscillation of Second Order Nonlinear Dynamic Equations

8.4. Oscillation of Perturbed Nonlinear Dynamic Equations

8.5. Positive Solutions of Nonlinear Dynamic Equations

8.6. Oscillation of Emden–Fowler Equations

8.7. Oscillation of First Order Delay Dynamic Equations

8.8. Oscillation of Symplectic Dynamic Systems

8.9. Notes

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