Rent this article via DeepDyve. Antonevich and V. Press, Cambridge, Mass. Google Scholar. Notes , 44 , No. MathSciNet Google Scholar. Notes , 63 , No. New York , , No. Beklaryan and M. Bellman and K. Cartan, Calcul Differentiel. Formes Differentielles , Hermann, Paris Chen, S. Pan, and J. Colonius, A. Manitius, and D.
Differential Equations , 78 , No. Daletskij and M. Ezzinbi and J. Stochastic Anal. Frenkel and T. USSR , 1 , — Hale and S. Ioffe and V. Equations , 12 , — We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact. 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 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 Linear differential difference equations. Functional differential equations: Basic theory. Author : V. Among the subjects treated are qualitative theory, stability, periodic solutions, optimal control and estimation, the theory of linear equations, and basic principles of mathematical modelling.
The work, which treats many concrete problems in detail, gives a good overview of the entire field and will serve as a stimulating guide to further research. Audience: This volume will be of interest to researchers and post graduate students working in analysis, and in functional analysis in particular. It will also appeal to mathematical engineers, industrial mathematicians, mathematical system theoreticians and mathematical modellers.
The interest here is on a geometric theory of FDE. In particular the equations of the retarded types are considered. As a consequence, it was decided not to make a few corrections and additions for a second edition of those notes, but to present a more compre hensive theory. The present work attempts to consolidate those elements of the theory which have stabilized and also to include recent directions of research.
The following chapters were not discussed in my original notes. Chapter 1 is an elementary presentation of linear differential difference equations with constant coefficients of retarded and neutral type. Chapter 4 develops the recent theory of dissipative systems. Chapter 9 is a new chapter on perturbed systems. Chapter 11 is a new presentation incorporating recent results on the existence of periodic solutions of autonomous equations.
Chapter 12 is devoted entirely to neutral equations. Chapter 13 gives an introduction to the global and generic theory.
There is also an appendix on the location of the zeros of characteristic polynomials. Linear autonomous equations. Periodic systems. Equations of neutral type. Near equilibrium and periodic orbits. Periodic solutions of autonomous equations. Additional topics. Back Matter Pages About this book Introduction The present book builds upon an earlier work of J. We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact.
A more complete theory of neutral equations is presented see Chapters 1, 2, 3, 9, and 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.
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