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Asymptotics of Linear Differential Equations

  • Book
  • © 2001

Overview

Authors:
  1. M. H. Lantsman
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Part of the book series: Mathematics and Its Applications (MAIA, volume 533)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • M. H. Lantsman
    Pages 1-13

  3. Metric Spaces

    • M. H. Lantsman
    Pages 14-37

  4. Asymptotic Spaces

    • M. H. Lantsman
    Pages 38-48

  5. Asymptotic Behavior of Functions

    • M. H. Lantsman
    Pages 49-89

  6. Power Order Growth Functions on the Positive Semi-Axis

    • M. H. Lantsman
    Pages 90-127

  7. Power Order Growth Functions of the Complex Argument

    • M. H. Lantsman
    Pages 128-143

  8. Integrals

    • M. H. Lantsman
    Pages 144-182

  9. Linear Differential Equations

    • M. H. Lantsman
    Pages 183-205

  10. General Asymptotic Properties of Linear Differential Equations

    • M. H. Lantsman
    Pages 206-229

  11. Linear Differential Equations with Power Order Growth Coefficients on the Positive Semi-Axis

    • M. H. Lantsman
    Pages 230-272

  12. Linear Differential Equations in Singular Cases on the Positive Semi-Axis

    • M. H. Lantsman
    Pages 273-306

  13. Linear Differential Equations in a Sector of the Complex Plane

    • M. H. Lantsman
    Pages 307-334

  14. Linear Differential Equations with Power-Logarithmic Coefficients

    • M. H. Lantsman
    Pages 335-353

  15. Linear Difference Equations. General Theory

    • M. H. Lantsman
    Pages 354-377

  16. Asymptotic Behaviour of Solutions of Linear Difference Equations

    • M. H. Lantsman
    Pages 378-419

  17. Supplement

    • M. H. Lantsman
    Pages 420-424

  18. Back Matter

    Pages 425-441
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Keywords

About this book

The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural sci­ ence bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymp­ totic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects.

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