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9789067643931

Countable Systems of Differential Equations

by ;
  • ISBN13:

    9789067643931

  • ISBN10:

    9067643939

  • Format: Hardcover
  • Copyright: 2003-11-01
  • Publisher: De Gruyter

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Summary

This monograph is devoted to the solution of various problems in the theory of differential equations in the space "M" of bounded numerical sequences (called countable systems). In particular, the general theory of countable systems, the theory of oscillating solutions, and the theory of countable systems with pulse action are treated.
Main attention is given to generalization of the results of numerous authors, obtained in recent years for finite-dimensional systems of different equations to the case of systems from the analysed class.
The book contains the following four chapters:
- General concepts of the theory of infinite systems of differential equations
- Invariant tori
- Reducibility of linear systems
- Impulsive systems
This book will be of value and interest to anyone working in this field of differential equations.

Table of Contents

Preface vii
General Concepts of the Theory of Infinite Systems of Differential Equations
1(48)
Theorems on Existence and Uniqueness of Solutions
1(10)
Truncation Method
11(4)
Solutions of the Linear System
15(5)
Matrizant of a Linear System
20(7)
Normal Autonomous Systems
27(5)
Periodic Solutions
32(17)
Invariant Tori
49(102)
Green Function
49(19)
Existence of a Smooth Invariant Torus
68(7)
Cl-Differentiability of the Invariant Torus
75(24)
The Case of Infinitely Many Angular Variables
99(16)
Theorem on Convergence of the Sequence of Invariant Tori
115(4)
Invariant Tori of Nonlinear Systems
119(14)
Exponential Attraction of Motions in a Neighborhood of the Invariant Torus of a System of Equations to Its Motions on the Torus
133(18)
Reducibility of Linear Systems
151(46)
Erugin and Floquet--Lyapunov Theorems
151(4)
Periodic Systems
155(8)
Systems with Almost Periodic Coefficients
163(12)
Quasiperiodic Systems with Unbounded Right-Hand Side
175(14)
Decomposition of Countable Systems
189(8)
Impulsive Systems
197(74)
Some Results of the Theory of Linear Systems
197(10)
Integral Sets and Invariant Tori
207(24)
Periodic Solutions for Impulsive Systems with Small Parameter
231(21)
Approximate Solution of the Periodic Problem of Control
252(19)
References 271

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