Stability by Fixed Point Theory for Functional Differential Equations

Preface ix 0 Introduction and Overview 1(12) 0.1 The Origin of the Work 1(2) 0.2 An Introductory Lecture 3(10) 1 Half-linear Equations 13(76) 1.1 Statement of the problem 13(4) 1.2 Background and definitions 17(9) 1.3 Stability:Liapunov, Perron, and Krasovskii 26(11) 1.4 The most elementary examples 37(12) 1.5 Ultimate Boundedness and Periodicity 49(8) 1.6 Fixed Points or Liapunov Functions 57(15) 1.7 Necessary and sufficient conditions 72(17) 2 Classical Problems, Harmless Perturbations 89(120) 2.1 The Cooke-Yorke Hypothesis 89(29) 2.2 Equations of Volterra-Levin Type 118(12) 2.3 Li rd's Equation and Liapunov Functions 130(12) 2.4 A Problem of R.A. Smith Type 142(14) 2.5 A Nonconvolution Levin Equation 156(9) 2.6 The Bernoulli Equation 165(12) 2.7 Liapunov-Perron-Krasovskii Equations 177(13) 2.8 Seifert's Example of Memory 190(10) 2.9 The Problem of Lurie 200(5) 2.10 The Sunflower Equation 205(4) 3 Borrowing Coefficients 209(34) 3.0 Introduction: Schauder's Theorem 209(1) 3.1 Highly Nonlinear Delay Equations 209(17) 3.2 Borrowing and Addition of Terms 226(17) 4 Schauder's Theorem: A Choice 243(22) 4.0 Introduction 243(2) 4.1 A Second Order Equation 245(8) 4.2 Some Cubic Equations 253(12) 5 Boundedness, Periodicity, and Stability 265(30) 5.0 Introduction 265(1) 5.1 The Bernoulli Equation Revisited 266(9) 5.2 Becker's Resolvent and Perron's Theorem 275(20) 6 Open Problems, Global Nonlinearities 295(12) 6.1 Open Problems 295(1) 6.2 Nonlinearities 296(11) 7 Appleby's Stochastic Perturbations 307(30) 7.0 Acknowledgment 307(1) 7.1 Introduction 307(2) 7.2 Stochastic preliminaries 309(6) 7.3 Stochastic version of Levin's problem 315(13) 7.4 Stochastic Cooke-Yorke problem 328(9) References 337(8) Author Index 345(2) Subject Index 347