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 . . . . . . . . . .
. .
