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E-raamat: Stability of Differential Equations with Aftereffect

(Perm State Technical University, Russia), (Perm State University, Russia)
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Stability of Differential Equations with AftereffectSuurem pilt
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Stability of Differential Equations with Aftereffect presents stability theory for differential equations concentrating on functional differential equations with delay, integro-differential equations, and related topics. The authors provide background material on the modern theory of functional differential equations and introduce some new flexible methods for investigating the asymptotic behaviour of solutions to a range of equations. The treatment also includes some results from the authors' research group based at Perm and provides a useful reference text for graduates and researchers working in mathematical and engineering science.

Arvustused

"The present monograph is an outcome of serious research spread over a few decades. The presentation is very lucid and readers can easily understand the material presented in this monograph. It is the reviewer's opinion that this monograph is a good resource for specialists as well as beginners in this fascinating field." -Mathematical Reviews, Issue 2004f

Introduction to the Series vii
Preface ix
Notations xiii
Functional Differential Equations
1(24)
Introduction
1(1)
Representatives of the Functional Differential Equations with Aftereffect
1(7)
Linear Functional Differential Equations with Aftereffect
8(11)
Comments and References
19(6)
Linear Analysis of D-stability
25(66)
Introduction
25(1)
Functional Spaces and D-stability
26(7)
D-stability and Classical Stability
33(9)
D-stability of Linear Systems with Distributed Aftereffect
42(6)
``W-method''
48(12)
Stability Tests for LFDE with Distributed Delay
60(15)
Stability Tests for Linear Equations of Neutral Type
75(11)
Comments and References
86(5)
Cauchy Matrix and Stability Condition
91(36)
Introduction
91(1)
Cauchy Matrix
92(4)
Generalized Semigroup Equality
96(3)
Equivalence of Various Types of Stability
99(6)
Estimates of the Cauchy Function
105(9)
Autonomous Equations
114(4)
Main Test of Stability
118(4)
Comments and References
122(5)
Bohl-Perron Type Theorems
127(36)
Introduction
127(1)
D-stability
128(4)
Exponential Stability
132(6)
Asymptotic Stability
138(5)
Functions with Finite Limit
143(4)
Asymptotically Periodic Solutions
147(2)
Strong B-stability
149(6)
Relationship between Strong and Uniform Exponential Stabilities
155(4)
Comments and References
159(4)
Nonlinear Systems
163(36)
Introduction
163(1)
Stability with Respect to Linear Approximation
164(12)
Stability Conditions for Some Classes of FDE with Aftereffect
176(8)
Functional-Integral Inequalities
184(12)
Comments and References
196(3)
References 199(22)
Index 221


N.V. Azbelev, P.M. Simonov
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
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