Regular variation and differential equations
This is the first book offering an application of regular variation to the qualitative theory of differential equations. The notion of regular variation, introduced by Karamata (1930), extended by several scientists, most significantly de Haan (1970), is a powerful tool in studying asymptotics in various branches of analysis and in probability theory. Here, some asymptotic properties (including non-oscillation) of solutions of second order linear and of some non-linear equations are proved by m…
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- Full title :Regular variation and differential equations / Vojislav Marić.
Summary
This is the first book offering an application of regular variation to the qualitative theory of differential equations. The notion of regular variation, introduced by Karamata (1930), extended by several scientists, most significantly de Haan (1970), is a powerful tool in studying asymptotics in various branches of analysis and in probability theory. Here, some asymptotic properties (including non-oscillation) of solutions of second order linear and of some non-linear equations are proved by means of a new method that the well-developed theory of regular variation has yielded. A good graduate course both in real analysis and in differential equations suffices for understanding the book.
Read More ↓Edition Statements
- Publication Date:©2000.
Publication Statements
- Publisher(s):Springer
- Place of Publication:Berlin
- Language:eng
- Publication Date:©2000.
The Physical Object
- Description:1 online resource (x, 127 pages)
Edition Identifiers
- ISBN:9783540465201, 3540465200
- DOI:10.1007/BFb0103952.
- oclc:ocn162121523
- LC Classification:QA3
- Dewey Decimal:510 s
Table of Contents
I Linear equations: Existence of regular solutions: Preliminaries -- The case f(x)<0 -- II- and I-varying solutions -- The case of f(x) of arbitrary sign -- Regular boundedness of solutions -- Generalizations -- Examples -- Comments -- Asymptotic behaviour of regular solutions: Slowly varying solutions -- The case of f(x) of arbitrary sign -- The case of f(x)<0 -- Regularly varying solutions -- On zeros of oscillating solutions. Examples -- Comments II Nonlinear equations: Equations of Thomas Fermi type: Introduction and preliminaries -- The case of regularly varying f and o/ -- The case of rapidly varying f or o/ -- An equations arising in boundary-layer theory: Introduction -- Existence and uniqueness -- Estimates and asymptotic behaviour of solutions -- Comments -- Appendix: Properties of regularly varying and related Functions -- References -- Index.
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