Functional Differential Equations with Infinite Delay

Yoshiyuki Hino, Satoru Murakami, Toshiki Naito (auth.)3540540849, 9783540540847, 0387540849

In the theory of functional differential equations with infinite delay, there are several ways to choose the space of initial functions (phase space); and diverse (duplicated) theories arise, according to the choice of phase space. To unify the theories, an axiomatic approach has been taken since the 1960’s. This book is intended as a guide for the axiomatic approach to the theory of equations with infinite delay and a culmination of the results obtained in this way. It can also be used as a textbook for a graduate course. The prerequisite knowledge is foundations of analysis including linear algebra and functional analysis. It is hoped that the book will prepare students for further study of this area, and that will serve as a ready reference to the researchers in applied analysis and engineering sciences.

---

Table of contents :
Phase Spaces….Pages 1-34
Fundamental theorems….Pages 35-52
Stieltjes integrals and linear operators on ℬ….Pages 53-98
General linear systems….Pages 99-129
Linear autonomous systems….Pages 130-176
Linear periodic systems….Pages 177-186
Fading memory spaces and functional differential equations….Pages 187-214
Stabilities in perturbed systems and limiting equations….Pages 215-253
Existence of periodic solutions and almost periodic solutions….Pages 254-276