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Introduction to Linear Systems of Differential Equations
L. Ya. Adrianova, St. Petersburg State University, Russia
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Translations of Mathematical Monographs
1995; 204 pp; hardcover
Volume: 146
ISBN-10: 0-8218-0328-X
ISBN-13: 978-0-8218-0328-8
List Price: US$93
Member Price: US$74.40
Order Code: MMONO/146
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The theory of linear systems of differential equations is one of the cornerstones of the whole theory of differential equations. At its root is the concept of the Lyapunov characteristic exponent.

In this book, Adrianova presents introductory material and further detailed discussions of Lyapunov exponents. She also discusses the structure of the space of solutions of linear systems. Classes of linear systems examined are from the narrowest to widest: 1) autonomous, 2) periodic, 3) reducible to autonomous, 4) nearly reducible to autonomous, 5) regular.

In addition, Adrianova considers the following:

  • stability of linear systems and the influence of perturbations of the coefficients on the stability
  • the criteria of uniform stability and of uniform asymptotic stability in terms of properties of the solutions
  • several estimates of the growth rate of solutions of a linear system in terms of its coefficients

How perturbations of the coefficients change all the elements of the spectrum of the system is definitely the most complicated and involved problem in the whole theory of linear systems. Introduction to Linear Systems of Differential Equations presents the proof of the necessary and sufficient conditions for stability of the exponents for the simplest case of a two-dimensional diagonal system.

Readership

Graduate students and research mathematicians interested in the theory of differential equations.

Reviews

"Gives a very good introduction to the theory of linear systems of differential equations ... One of the best features of the book is the very large number of examples ... suitable for research and graduate students working in the theory of differential equations and in mathematical applications ... gives a good foundation for the study of more involved and specialized parts of the theory of linear differential equations."

-- Zentralblatt MATH

Table of Contents

  • Linear autonomous and periodic systems
  • Lyapunov characteristic exponents in the theory of linear systems
  • Reducible, almost reducible, and regular systems
  • Stability and small perturbations of the coefficients of linear systems
  • On the variation of characteristic exponents under small perturbations of coefficients
  • A linear homogeneous equation of the second order
  • Appendix
  • References
  • Index
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