Countable systems of differential equations / A.M. Samoilenko and Yu. V. Teplinskii.

Format:

Book

Author/Creator:

Samoĭlenko, A. M. (Anatoliĭ Mikhaĭlovich)

Contributor:

Teplinskii, Yu. V.

Rosengarten Family Fund.

Language:

English

Subjects (All):

Differential equations.

Linear systems.

Invariant manifolds.

Physical Description:

viii, 287 pages ; 25 cm

Place of Publication:

Utrecht ; Boston : VSP, 2003.

Summary:

This book is devoted to the solution of various problems in the theory of differential equations in a space M of bounded numerical sequences (called countable systems). In particular, the book deals with the general theory of countable systems, the theory of oscillating solutions, and the theory of countable systems with pulse action. Special attention is given to the generalization of recent results for finite-dimensional systems of differential equations to the case of systems from the analyzed class. Chapters cover general concepts of the theory of infinite systems of differential equations, invariant tori, reducibility of linear systems, and impulsive systems. Author information is not given, and there is no subject index. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

Contents:

1. General Concepts of the Theory of Infinite Systems of Differential Equations 1

1.1. Theorems on Existence and Uniqueness of Solutions 1

1.2. Truncation Method 11

1.3. Solutions of the Linear System 15

1.4. Matrizant of a Linear System 20

1.5. Normal Autonomous Systems 27

1.6. Periodic Solutions 32

2. Invariant Tori 49

2.7. Green Function 49

2.8. Existence of a Smooth Invariant Torus 68

2.9. C[superscript l]-Differentiability of the Invariant Torus 75

2.10. The Case of Infinitely Many Angular Variables 99

2.11. Theorem on Convergence of the Sequence of Invariant Tori 115

2.12. Invariant Tori of Nonlinear Systems 119

2.13. Exponential Attraction of Motions in a Neighborhood of the Invariant Torus of a System of Equations to Its Motions on the Torus 133

3. Reducibility of Linear Systems 151

3.14. Erugin and Floquet-Lyapunov Theorems 151

3.15. Periodic Systems 155

3.16. Systems with Almost Periodic Coefficients 163

3.17. Quasiperiodic Systems with Unbounded Right-Hand Side 175

3.18. Decomposition of Countable Systems 189

4. Impulsive Systems 197

4.19. Some Results of the Theory of Linear Systems 197

4.20. Integral Sets and Invariant Tori 207

4.21. Periodic Solutions for Impulsive Systems with Small Parameter 231

4.22. Approximate Solution of the Periodic Problem of Control 252.

Notes:

Includes bibliographical references (pages 271-287).

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

ISBN:

9067643939

OCLC:

53903485