Introduction to Functional Differential EquationsSpringer Science & Business Media, 21.11.2013 - 450 Seiten The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in 1977. We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a complete new presentation of lin ear systems (Chapters 6~9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global at tractors was completely revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (see Chapters 1, 2, 3, 9, and 10). Chapter 12 is completely new and contains a guide to active topics of re search. In the sections on supplementary remarks, we have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive. Jack K. Hale Sjoerd M. Verduyn Lunel Contents Preface............................................................ v Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 1. Linear differential difference equations . . . . . . . . . . . . . . 11 . . . . . . 1.1 Differential and difference equations. . . . . . . . . . . . . . . . . . . . 11 . . . . . . . . 1.2 Retarded differential difference equations. . . . . . . . . . . . . . . . 13 . . . . . . . 1.3 Exponential estimates of x( ¢,f) . . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . . . 1.4 The characteristic equation . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . 1.5 The fundamental solution. . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . 1.6 The variation-of-constants formula............................. 23 1. 7 Neutral differential difference equations . . . . . . . . . . . . . . . . . 25 . . . . . . . 1.8 Supplementary remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . 34 . . . . . . . . . . . . . 2. Functional differential equations: Basic theory . . . . . . . . 38 . . 2.1 Definition of a retarded equation. . . . . . . . . . . . . . . . . . . . . . 38 . . . . . . . . . 2.2 Existence, uniqueness, and continuous dependence . . . . . . . . . . 39 . . . 2.3 Continuation of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 44 . . . . . . . . . . . . |
Inhalt
1 | |
11 | |
Basic theory | 38 |
Properties of the solution map | 67 |
Autonomous and periodic processes | 100 |
Stability theory | 130 |
General linear systems | 167 |
Linear autonomous equations | 193 |
Periodic systems | 236 |
Equations of neutral type | 255 |
Near equilibrium and periodic orbits | 302 |
Periodic solutions of autonomous equations | 331 |
Additional topics | 364 |
Stability of characteristic equations | 414 |
444 | |
Andere Ausgaben - Alle anzeigen
Introduction to Functional Differential Equations Jack K. Hale,Sjoerd M. Verduyn Lunel Eingeschränkte Leseprobe - 1993 |
Introduction to Functional Differential Equations Jack K. Hale,Sjoerd M. Verduyn Lunel Keine Leseprobe verfügbar - 2013 |
Häufige Begriffe und Wortgruppen
asymptotically stable attractor autonomous Ax(t Banach space bounded sets bounded variation Bx(t Chapter characteristic equation characteristic multiplier compact set completely continuous continuous function continuously differentiable Corollary corresponding decomposition defined definition delay denotes derivative differential difference equations eigenspace eigenvalues equa Equation 1.1 equilibrium point equivalent example existence exponential finite fixed point following result functional differential equations Furthermore given global attractor Hale hyperbolic hypotheses implies initial data interval invariant set Jordan chains Laplace transform Lemma Liapunov functionals linear equation manifold matrix neighborhood NFDE NFDE(D obtain one-to-one ordinary differential equations periodic orbit periodic solution perturbation point dissipative positive constants precompact problem proof of Theorem properties prove RFDE RFDE(ƒ scalar Section semigroup small solutions solution of Equation solution operator subset subspace Suppose Theorem 3.1 theory tion variation-of-constants formula vector