Oscillation theory for functional differential equations

Cover......Page 1
Title......Page 8
Preface......Page 10
Contents......Page 12
1.0. Introduction......Page 15
1.1. Initial Value Problems......Page 16
1.2. Oscillation and Nonoscillation......Page 18
1.3. Formulation of Boundary Value Problems for Functional Differential Equations......Page 20
1.4. Fixed Point Theorems......Page 22
2.0. Introduction......Page 28
2.1. Stable Type Equations with a Single Delay......Page 29
2.2. The Distribution of Zeros of Oscillatory Solutions......Page 45
2.3. Unstable Type Equations......Page 51
2.4. Equations with Oscillatory Coefficients......Page 54
2.5. Equations with Positive and Negative Coefficients......Page 59
2.6. Equations with Several Delays......Page 64
2.7. Equations with Forced Terms......Page 85
2.8. Single Population Models with Delays......Page 90
2.9. Notes......Page 107
3.0. Introduction......Page 109
3.1. Characteristic Equations......Page 111
3.2. Equations with Variable Coefficients (I)......Page 124
3.3. Equations with Variable Coefficients (II)......Page 149
3.4. Comparison Results......Page 170
3.5. Unstable Type Equations......Page 174
3.6. Sublinear Equations......Page 182
3.7. Equations with Mixed Coefficients......Page 189
3.8. Linearized Oscillation......Page 199
3.9. Equations with a Nonlinear Neutral Term......Page 205
3.10. Forced Equations......Page 211
3.11. Notes......Page 214
4.0. Introduction......Page 216
4.1. Linearized Oscillation......Page 217
4.2. Existence of Oscillatory Solutions......Page 224
4.3. Sturm Comparison Theorems......Page 233
4.4. Oscillation Criteria......Page 240
4.5. Classification o f Nonoscillatory Solutions......Page 256
4.6. Unstable Type Equations......Page 269
4.7. Forced Oscillation......Page 286
4.8. Equations with a Nonlinear Neutral Term......Page 292
4.9. Advanced Type Equations......Page 298
4.10. Notes......Page 301
5.0. Introduction......Page 302
5.1. Comparison Theorems for Odd Order Equations......Page 303
5.2. Oscillation and Nonoscillation of Odd Order Equations......Page 316
5.3. Oscillation of Even Order Equations......Page 331
5.4. Classification of Nonoscillatory Solutions......Page 338
5.5. Existence of Oscillatory Solutions......Page 354
5.6. Equations with Nonlinear Neutral Terms......Page 361
5.7. Unstable Type Equations......Page 371
5.8. Notes......Page 387
6.0. Introduction and Preliminaries......Page 388
6.1. Systems with Constant Matrix Coefficients......Page 391
6.2. Systems with Variable Matrix Coefficients......Page 403
6.3. Comparison with Scalar Equations......Page 410
6.4. Existence of Nonoscillatory Solutions......Page 414
6.5. Notes......Page 427
7.0. Introduction......Page 428
7.1. Lipschitz Type Conditions......Page 429
7.2. Nagumo Type Condition......Page 436
7.3. Leray-Schauder Alternative......Page 443
7.4. Topological Transversality Method......Page 455
7.5. Boundary Value Problems for Singular Equations......Page 466
7.6. Notes......Page 478
References......Page 479
Index......Page 496