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E-raamat: Advances in Stability Theory at the End of the 20th Century

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This volume presents surveys and research papers on various aspects of modern stability theory, including discussions on modern applications of the theory, all contributed by experts in the field. The volume consists of four sections that explore the following directions in the development of stability theory: progress in stability theory by first approximation; contemporary developments in Lyapunov's idea of the direct method; the stability of solutions to periodic differential systems; and selected applications. Advances in Stability Theory at the End of the 20th Century will interest postgraduates and researchers in engineering fields as well as those in mathematics.
Introduction to the Series ix
Preface xi
An Overview xiii
Part 1 Progress in Stability Theory by the First Approximation
Invariant Foliations for Caratheodory Type Differential Equations in Banach Spaces
1(14)
B. Aulbach
T. Wanner
On Exponential Asymptotic Stability for Functional Differential Equations with Causal Operators
15(10)
C. Corduneanu
Yizeng Li
Lyapunov Problems on Stability by Linear Approximation
25(24)
N.A. Izobov
Part 2 Contemporary Development of Lyapunov's Ideas of Direct Method
Vector Lyapunov Functions Nonlinear, Time-Varying, Ordinary and Functional Differential Equations
49(26)
P. Borne
M. Dambrine
W. Perruquetti
J.P. Richard
Some Results on Total Stability Properties for Singular Systems
75(14)
A. D'Anna
Stability Theory of Volterra Difference Equations
89(18)
F. Dannan
S. Elaydi
P. Li
Consistent Lyapunov Methodology for Exponential Stability: PCUP Approach
107(14)
Ly. T. Gruyitch
Advances in Stability Theory of Lyapunov: Old and New
121(14)
V. Lakshmikantham
S. Leela
Matrix Liapunov Functions and Stability Analysis of Dynamical Systems
135(18)
A.A. Martynyuk
Stability Theorems in Impulsive Functional Differential Equations with Infinite Delay
153(22)
A.A. Martynyuk
J.H. Shen
I. P. Stavroulakis
The Asymptotic Behaviour of Solutions of Stochastic Functional Differential Equations with Finite Delays by Liapunov-Razumikhin Method
175(14)
T. Taniguchi
A Non-Standard Approach to the Study of the Dynamic System Stability
189(12)
V.A. Vujicic
Part 3 Stability of Solutions to Periodic Differential Systems
A Survey of Starzhinskii's Works on Stability of Periodic Motions and Nonlinear Oscillations
201(16)
Yu.A. Mitropol'skii
A.A. Martynyuk
V.I. Zhukovskii
Implications of the Stability of an Orbit for Its Omega Limit Set
217(14)
J.S. Muldowney
Some Concepts of Periodic Motions and Stability Originated by Analysis of Homogeneous Systems
231(12)
V.N. Pilipchuk
Stability Criteria for Periodic Solutions of Autonomous Hamiltonian Systems
243(12)
A.A. Zevin
Part 4 Selected Applications
Stability in Models of Agriculture--Industry--Environment Interactions
255(12)
H.I. Freedman
M. Solomonovich
L.P. Apedaile
A. Hailu
Bifurcations of Periodic Solutions of the Three Body Problem
267(22)
V.I. Gouliaev
Complex Mechanical Systems: Steady-State Motions, Oscillations, Stability
289(32)
A. Yu. Ishlinsky
V.A. Storozhenko
M.E. Temchenko
Progress in Stability of Impulsive Systems with Applications to Population Growth Models
321(18)
Xinzhi Liu
Index 339
A.A. Martynyuk
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