Linear systems of ordinary differential equations with periodic and quasi-periodic coefficients : (with revisions by the author for the English edition) / [by] Nikolay P. Erugin ; translated by Scripta Technica, Inc. ; translation editor, Richard Bellman.

Format:

Book

Author/Creator:

Erugin, N. P. (Nikolaĭ Pavlovich), author.

Contributor:

Scripta Technica, inc., translator.

Bellman, Richard, 1920-1984, editor.

Series:

Mathematics in science and engineering ; volume 28.

Mathematics in science and engineering ; volume 28

Standardized Title:

Lineĭnye sistemy obyknovennykh different͡sialnykh uravnenii. English

Language:

English

Subjects (All):

Differential equations, Linear.

Physical Description:

1 online resource (295 p.)

Place of Publication:

New York : Academic Press, 1966.

Language Note:

English

Summary:

Linear systems of ordinary differential equations, with periodic and quasi-periodic coefficients

Contents:

Front Cover; Linear Systems of Ordinary Differential Equations; Copyright Page; Author's Comments; Contents; Introduction; Chapter 1. Functions of a Single Matrix; Chapter 2. Auxiliary Theorems; Chapter 3. Functions of Several Matrices and of a Countable Set of Matrices; Chapter 4. Classes of Systems of Linear Differential Equations That Can Be Integrated in Closed Form; Chapter 5. Other Systems of Linear Differential Equations That Are Integrable in Closed Form

Chapter 6. The Construction of Solutions of Certain Linear Systems of Differential Equations in the Form of a Series of Several Matrices (of a Series of Compositions)Chapter 7. Solution of the Poincaré-Lappo-Danilevskiy Problem; Chapter 8. Formulation of Certain Problems of Linear Systems of Differential Equations with Real Periodic Coefficients; Chapter 9. Solution of the Problems Posed in Section 8 on the Basis of Real Functions; Chapter 10. Expansion of an Exponential Matrix in a Series of Powers of a Parameter

Chapter 11. Determination of the Coefficients in the Series Expansion of an Exponential MatrixChapter 12. Approximate Integration of Equation (10.1); Chapter 13. The Case in Which P0 (t), P1 (t), ..., Pm (t) in Equation (10.1) Are Constants; Chapter 14. The Case in Which P0 is Constant and expP0t is a Periodic Matrix in Equation (10.1); Chapter 15. An Example Illustrating Section 14; Chapter 16. Canonical Systems; Chapter 17. The System (16.3) With P0 = P1 = ... = Pm-1=0; Chapter 18. Artem'yev's Problem; Chapter 19. The Theory of Reducible Systems; Chapter 20. Shtokalo's Method

Chapter 21. Determination of the Coefficients of the Series (20.22) and (20.23) by Shtokalo's Method [10, 38]Chapter 22. Approximate Solutions Obtained by Shtokalo's Method; Chapter 23. Inequalities Following from Shtokalo's Method; Chapter 24. Shtokalo's Theorem. Inequalities Involving Approximate Solutions Found by Shtokalo's Method (for Linear and Nonlinear Systems). Particular Problems; Chapter 25. Other Approximate Forms of Solutions That .Arise From Shtokalo's and Bogolyubov's Methods; Chapter 26. Demidovich's Problem

Chapter 27. Another Formulation of Certain Problems and Consequences of ThemChapter 28. Solution of the Problems in Section 8 by Use of the Method of Solving the Poincaré-Lappo-DaniIevskiy Problem and Lyapunov's Contributions; Chapter 29. Remarks on Bounded and Periodic Solutions of a System of Two Differential Equations With Periodic Coefficients; Chapter 30. Periodic and Bounded Solutions of the Systems of Equations Considered in Sections 3 and 4

Chapter 31. Questions Involving the Boundedness and Periodicity of Solutions of a System of Two Linear Differential Equations With the Aid of a Special Exponential Substitution Obtained by Lappo-Danilevskiy

Notes:

Translation of: Lineynyye sistemy obyknovennykh differentsial'nykh uravneniy s periodicheskimi i kvaziperiodicheskimi koeffitsiyentami.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9786612769795

9781282769793

1282769790

9780080955353

0080955355

OCLC:

699474127