Mathematics and its Applications

Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients

Authors: Mitropolsky, Yuri A., Samoilenko, Anatolii M., Van Twist, Mark J.W.

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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.

Table of contents (6 chapters)

  • Numerical-Analytic Method of Investigation of Periodic Solutions for Systems with Aftereffect

    Mitropolsky, Yu A. (et al.)

    Pages 1-75

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

    Mitropolsky, Yu A. (et al.)

    Pages 77-106

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

    Mitropolsky, Yu A. (et al.)

    Pages 107-134

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

    Mitropolsky, Yu A. (et al.)

    Pages 135-200

  • Reducibility of Linear Systems of Difference Equations with Quasiperiodic Coefficients

    Mitropolsky, Yu A. (et al.)

    Pages 201-222

Buy this book

eBook $84.99
price for USA (gross)
  • ISBN 978-94-011-2728-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.00
price for USA
  • ISBN 978-94-010-5210-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients
Authors
Series Title
Mathematics and its Applications
Series Volume
87
Copyright
1993
Publisher
Springer Netherlands
Copyright Holder
Kluwer Academic Publishers
eBook ISBN
978-94-011-2728-8
DOI
10.1007/978-94-011-2728-8
Softcover ISBN
978-94-010-5210-8
Series ISSN
0169-6378
Edition Number
1
Number of Pages
XIV, 280
Topics