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Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients

  • Book
  • © 1993

Overview

Authors:
  1. Yu A. Mitropolsky

    1. Institute of Mathematics, C.I.S., Kiev, Ukraine

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  2. A. M. Samoilenko

    1. Institute of Mathematics, C.I.S., Kiev, Ukraine

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    You can also search for this author in PubMed   Google Scholar

  3. D. I. Martinyuk

    1. Institute of Mathematics, C.I.S., Kiev, Ukraine

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Part of the book series: Mathematics and its Applications (MASS, volume 87)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Numerical-Analytic Method of Investigation of Periodic Solutions for Systems with Aftereffect

    • Yu A. Mitropolsky, A. M. Samoilenko, D. I. Martinyuk
    Pages 1-75

  3. Investigation of Periodic Solutions of Systems with Aftereffect by Bubnovgalerkin’s Method

    • Yu A. Mitropolsky, A. M. Samoilenko, D. I. Martinyuk
    Pages 77-106

  4. Quasiperiodic Solutions of Systems with Lag. Bubnov-Galerkin’s Method

    • Yu A. Mitropolsky, A. M. Samoilenko, D. I. Martinyuk
    Pages 107-134

  5. Existence of Invariant Toroidal Manifolds for Systems with Lag. Investigation of The Behavior of Trajectories in their Vicinities

    • Yu A. Mitropolsky, A. M. Samoilenko, D. I. Martinyuk
    Pages 135-200

  6. Reducibility of Linear Systems of Difference Equations with Quasiperiodic Coefficients

    • Yu A. Mitropolsky, A. M. Samoilenko, D. I. Martinyuk
    Pages 201-222

  7. Invariant Toroidal Sets for Systems of Difference Equations. Investigation of the Behavior of Trajectories on Toroidal Sets and in their Vicinities

    • Yu A. Mitropolsky, A. M. Samoilenko, D. I. Martinyuk
    Pages 223-261

  8. Back Matter

    Pages 263-280
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Keywords

About this book

Many problems in celestial mechanics, physics and engineering involve the study of oscillating systems governed by nonlinear ordinary differential equations or partial differential equations. This volume represents an important contribution to the available methods of solution for such systems.
The contents are divided into six chapters. Chapter 1 presents a study of periodic solutions for nonlinear systems of evolution equations including differential equations with lag, systems of neutral type, various classes of nonlinear systems of integro-differential equations, etc. A numerical-analytic method for the investigation of periodic solutions of these evolution equations is presented. In Chapters 2 and 3, problems concerning the existence of periodic and quasiperiodic solutions for systems with lag are examined. For a nonlinear system with quasiperiodic coefficients and lag, the conditions under which quasiperiodic solutions exist are established. Chapter 4 is devoted to the study of invariant toroidal manifolds for various classes of systems of differential equations with quasiperiodic coefficients. Chapter 5 examines the problem concerning the reducibility of a linear system of difference equations with quasiperiodic coefficients to a linear system of difference equations with constant coefficients.
Chapter 6 contains an investigation of invariant toroidal sets for systems of difference equations with quasiperiodic coefficients.
For mathematicians whose work involves the study of oscillating systems.

Authors and Affiliations

  • Institute of Mathematics, C.I.S., Kiev, Ukraine

    Yu A. Mitropolsky, A. M. Samoilenko, D. I. Martinyuk

Bibliographic Information

  • Book Title: Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients

  • Authors: Yu A. Mitropolsky, A. M. Samoilenko, D. I. Martinyuk

  • Series Title: Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-94-011-2728-8

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Kluwer Academic Publishers 1993

  • Hardcover ISBN: 978-0-7923-2054-8Published: 30 November 1992

  • Softcover ISBN: 978-94-010-5210-8Published: 22 November 2012

  • eBook ISBN: 978-94-011-2728-8Published: 06 December 2012

  • Series ISSN: 0169-6378

  • Edition Number: 1

  • Number of Pages: XIV, 280

  • Topics: Ordinary Differential Equations, Partial Differential Equations, Applications of Mathematics

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