Overview

This book is devoted to the asymptotic theory of differential equations. Asymptotic theory is an independent and important branch of mathematical analysis that began to develop at the end of the 19th century. Asymptotic methods' use of several important phenomena of nature can be explained. The main problems considered in the text are based on the notion of an asymptotic space, which was introduced by the author in his works. Asymptotic spaces for asymptotic theory play analogous roles as metric spaces for functional analysis. It allows one to consider many (seemingly) miscellaneous asymptotic problems by means of the same methods and in a compact general form. The book contains the theoretical material and general methods of its application to many partial problems, as well as several new results of asymptotic behavior of functions, integrals, and solutions of differential and difference equations. Audience: The material will be of interest to mathematicians, researchers, and graduate students in the fields of ordinary differential equations, finite differences and functional equations, operator theory, and functional analysis.

Full Product Details

Author:   M.H. Lantsman
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of hardcover 1st ed. 2001
Volume:   533
Dimensions:   Width: 16.00cm , Height: 2.30cm , Length: 24.00cm
Weight:   0.688kg
ISBN:  

9789048157730

ISBN 10:   9048157730
Pages:   441
Publication Date:   06 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

1. Introduction.- 2. Metric spaces.- 3. Asymptotic spaces.- 4. Asymptotic behaviour of functions.- 5. Power order growth functions on the positive semi-axis.- 6. Power order growth functions of the complex argument.- 7. Integrals.- 8. Linear differential equations.- 9. General asymptotic properties of linear differential equations.- 10. Linear differential equations with power order growth coefficients on the positive semi-axis.- 11. Linear differential equations in singular cases on the positive semi-axis.- 12. Linear differential equations in a sector of the complex plane.- 13. Linear differential equations with power-logarithmic coefficients.- 14. Linear difference equations. General theory.- 15. Asymptotic behaviour of solutions of linear difference equations.- 16. Supplement.- List of symbols.

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