| Preface | p. xi |
| Preliminaries | |
| Introduction | p. 1 |
| Continuability, Boundedness and Convergence to Zero | p. 2 |
| Some Useful Results from Analysis and Fixed Point Theorems | p. 10 |
| Notes and General Discussions | p. 12 |
| References | p. 12 |
| Oscillation and Nonoscillation of Linear Ordinary Differential Equations | |
| Introduction | p. 13 |
| Sturm Comparison Theorem | p. 13 |
| Nonoscillatory Characterizations and Comparison Theorems | p. 15 |
| Nonoscillation Criteria | p. 25 |
| Oscillation Criteria | p. 35 |
| Oscillation Criteria-Integral Averaging | p. 40 |
| Oscillation Criteria-Integrable Coefficients | p. 70 |
| Forced Oscillations | p. 82 |
| Notes and General Discussions | p. 90 |
| References | p. 91 |
| Oscillation and Nonoscillation of Half-Linear Differential Equations | |
| Introduction | p. 93 |
| Preliminaries | p. 94 |
| Sturm-Type Comparison Theorems | p. 94 |
| Levin-Type Comparison Theorems | p. 100 |
| Liapunov's Inequality | p. 105 |
| An Oscillation Criterion for Almost-Periodic Sturm-Liouville Equations | p. 107 |
| On Zeros of Solutions of a Singular Half-linear Differential Equation | p. 113 |
| Nonoscillation Criteria | p. 140 |
| Nonoscillatory Characterization | p. 140 |
| Comparison Theorems | p. 147 |
| Sufficient Conditions for Nonoscillation of Equation (3.1.1) | p. 148 |
| Further Results on Nonoscillation of Equation (3.1.1) | p. 154 |
| Oscillation Criteria | p. 163 |
| Oscillation Criteria-Integral Averaging | p. 168 |
| Oscillation Theorems for Equation (3.1.1) | p. 168 |
| Interval Criteria for the Oscillation of Equation (3.1.1) | p. 179 |
| The Weighted-Average Oscillation Criteria | p. 188 |
| Oscillation Criteria-Integrable Coefficients | p. 196 |
| Oscillation of Damped and Forced Equations | p. 205 |
| Oscillation of Equation (3.11.1) | p. 206 |
| Oscillation of Equation (3.11.2) | p. 207 |
| Distance of Zeros of Oscillatory Solutions | p. 210 |
| Oscillation and Nonoscillation of Half-linear Equations with Deviating Arguments | p. 218 |
| Some Useful Lemmas | p. 219 |
| Oscillation of Equation (3.13.1) | p. 223 |
| Some Extensions and More Oscillation Criteria | p. 232 |
| Classification of Nonoscillatory Solutions | p. 237 |
| A Comparison Theorem | p. 251 |
| Oscillation of Equation (3.13.2) | p. 253 |
| Nonoscillation of Solutions of Equation (3.13.127) | p. 259 |
| Notes and General Discussions | p. 267 |
| References | p. 268 |
| Oscillation Theory for Superlinear Differential Equations | |
| Introduction | p. 273 |
| Superlinear Oscillation Criteria | p. 273 |
| Further Results on Superlinear Oscillations | p. 296 |
| Existence of Nonoscillatory Solutions and Comparison Results | p. 328 |
| A Necessary Condition for Oscillation | p. 328 |
| Comparison of Nonlinear Equations of the Same Form | p. 332 |
| Linearization of Oscillation Theorems | p. 339 |
| Oscillation Criteria for Certain Nonlinear Differential Equations | p. 341 |
| Superlinear Forced Oscillations | p. 358 |
| Oscillation of Nonlinear Differential Equations with Nonlinear Damping Term | p. 362 |
| Damping with Nonlinear Growth-Oscillation Criteria | p. 362 |
| Damping with Nonlinear Growth-A Nonoscillation Theorem | p. 367 |
| Notes and General Discussions | p. 371 |
| References | p. 372 |
| Oscillation Theory for Sublinear Differential Equations | |
| Introduction | p. 376 |
| Sublinear Oscillation Criteria | p. 376 |
| Further Sublinear Oscillation Criteria | p. 387 |
| Linearization of Sublinear Oscillation Theorems | p. 429 |
| Nonoscillation Theorems for Sublinear Differential Equations | p. 433 |
| Oscillation Criteria for Certain Nonlinear Differential Equations | p. 444 |
| Notes and General Discussions | p. 453 |
| References | p. 453 |
| Further Results on the Oscillation of Differential Equations | |
| Introduction | p. 457 |
| Oscillation Criteria of Olech-Opial-Wazewski Type | p. 457 |
| Some Definitions and Notation | p. 458 |
| Oscillation Criteria | p. 459 |
| Further Results | p. 463 |
| Oscillation Criteria for Half-linear Differential Equations | p. 466 |
| Preliminary Results | p. 467 |
| Oscillation Criteria | p. 469 |
| Oscillation Criteria via Liapunov's Second Method | p. 476 |
| Preliminaries | p. 477 |
| Oscillation Criteria | p. 479 |
| Notes and General Discussions | p. 489 |
| References | p. 490 |
| Oscillation Results for Differential Systems | |
| Introduction | p. 491 |
| Oscillation of Nonlinear Two-dimensional Differential Systems | p. 491 |
| Superlinear Case | p. 493 |
| Sublinear Case | p. 498 |
| Further Oscillation Criteria | p. 500 |
| Oscillation Theorems for Linear Differential Systems | p. 503 |
| Oscillation Theorems for Differential Systems with Functionally Commutative Matrix Coefficients | p. 533 |
| Comparison Theorems for Operator-Valued Linear Differential Equations | p. 540 |
| Oscillation Results for Differential Systems with Forcing Terms | p. 549 |
| Notes and General Discussions | p. 552 |
| References | p. 554 |
| Asymptotic Behavior of Solutions of Certain Differential Equations | |
| Introduction | p. 558 |
| Asymptotic Behavior of Solutions of Nonlinear Differential Equations | p. 558 |
| Asymptotic Behavior of Nonoscillatory Solutions | p. 559 |
| Bounded Asymptotically Linear Solutions | p. 562 |
| Unbounded Asymptotically Linear Solutions | p. 567 |
| Further Extensions and Improvements | p. 574 |
| Asymptotic Behavior of Positive Solutions of Singular Emden-Fowler-Type Equations | p. 584 |
| Positive Solutions of Equation (8.2.1) | p. 585 |
| Positive Decaying Solutions of Equation (8.2.2) | p. 595 |
| Positive Solutions of Singular Emden-Fowler-Type Systems | p. 614 |
| Notes and General Discussions | p. 622 |
| References | p. 624 |
| Miscellaneous Topics | |
| Introduction | p. 625 |
| Comparison and Nonoscillation Results | p. 625 |
| Nonoscillatory Solutions of Forced Differential Equations | p. 632 |
| Limit Circle Criteria and Related Properties for Nonlinear Equations | p. 638 |
| Properties of Certain Differential Equations | p. 650 |
| Notes and General Discussions | p. 654 |
| References | p. 654 |
| Nonoscillation Theory for Multivalued Differential Equations | |
| Introduction | p. 656 |
| Preliminaries | p. 656 |
| Differential Inclusions | p. 657 |
| Neutral Inclusions | p. 664 |
| Notes and General Discussions | p. 668 |
| References | p. 668 |
| Subject Index | p. 670 |
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