Differential and Integral Inequalities: Functional Partial, Abstract and Complex Differential Equations v. 2: Theory and Applications: Functional

Front Cover......Page 1 Differential and Integral Inequalities......Page 4 Copyright Page......Page 5 Preface......Page 6 Contents......Page 8 PART 1: FUNCTIONAL DIFFERENTIAL EQUATIONS......Page 14 6.0 Introduction......Page 16 6.1 Existence......Page 17 6.2 Approximate Solutions and Uniqueness......Page 22 6.3 Upper Bounds......Page 26 6.4 Dependence on Initial Values and Parameters......Page 31 6.5 Stability Criteria......Page 34 6.6 Asymptotic Behavior......Page 37 6.7 A Topological Principle......Page 42 6.8 Systems with Repulsive Forces......Page 45 6.9 Functional Differential Inequalities......Page 47 6.10 Notes......Page 55 7.1 Stability Criteria......Page 56 7.2 Converse Theorems......Page 62 7.3 Autonomous Systems......Page 71 7.4 Perturbed Systems......Page 75 7.5 Extreme Stability......Page 79 7.6 Almost Periodic Systems......Page 85 7.7 Notes......Page 93 8.1 Basic Comparison Theorems......Page 94 8.2 Stability Criteria......Page 100 8.3 Perturbed Systems......Page 110 8.4 An Estimate of Time Lag......Page 113 8.5 Eventual Stability......Page 114 8.6 Asymptotic Behavior......Page 118 8.7 Notes......Page 123 PART 2: PARTIAL DIFFERENTIAL EQUATIONS......Page 124 9.1 Partial Differential Inequalities of First Order......Page 126 9.2 Comparison Theorems......Page 131 9.3 Upper Bounds......Page 140 9.4 Approximate Solutions and Uniqueness......Page 147 9.5 Systems of Partial Differential Inequalities of First Order......Page 149 9.6 Lyapunov-Like Function......Page 157 9.7 Notes......Page 161 10.1 Parabolic Differential Inequaliies in Bounded Domains......Page 162 10.2 Comparison Theorems......Page 168 10.3 Bounds, Under and Over Functions......Page 176 10.4 Approximate Solutions and Uniqueness......Page 183 10.5 Stability of Steady-State Solutions......Page 187 10.6 Systems of Parabolic Differential inequalities in Bounded Domains......Page 194 10.7 Lyapunov-Like Functions......Page 199 10.8 Stahility and Boundedness......Page 203 10.9 Conditional Stability and Boundedness......Page 213 10.10 Parabolic Differential Inequalities in Unbounded Domains......Page 218 10.11 Uniqueness......Page 223 10.12 Exterior Boundary-Value Problem and Uniqueness......Page 226 10.13 Notes......Page 232 11.1 Hyperbolic Diflerential Inequalities......Page 234 11.2 Uniqueness Criteria......Page 236 11.3 Upper Bounds and Error Estimates......Page 242 11.4 Notes......Page 246 PART 3: DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES......Page 248 12.1 Existence......Page 250 12.2 Nonlocal Existence......Page 254 12.3 Uniqueness......Page 256 12.4 Continuous Dependence and the Method of Averaging......Page 260 12.5 Existence (continued)......Page 262 12.6 Approximate Solutions and Uniqueness......Page 267 12.7 Chaplygin’s Method......Page 271 12.8 Asymptotic Behavior......Page 277 12.9 Lyapunov Function and Comparison Theorems......Page 280 12.10 Stability and Boundedness......Page 282 12.11 Notes......Page 285 PART 4: COMPLEX DIFFERENTIAL EQUATIONS......Page 286 13.1 Existence, Approximate Solutions, and Uniqueness......Page 288 13.2 Singularity-Free Regions and Growth Estimates......Page 292 13.3 Componentwise Bounds......Page 297 13.4 Lyapunov-like Functions and Comparison Theorems......Page 299 13.5 Notes......Page 301 Bibliography......Page 302 Author Index......Page 328 Subject Index......Page 331