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- catalog abstract "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.".
- catalog contributor b11650750.
- catalog created "2000.".
- catalog date "2000".
- catalog date "2000.".
- catalog dateCopyrighted "2000.".
- catalog description "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.".
- catalog description "Includes bibliographical references ([119]-124 p.) and index.".
- catalog description "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.".
- catalog extent "x, 127 p. ;".
- catalog identifier "3540671609 (softcover : alk. paper)".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1726.".
- catalog isPartOf "Lecture notes in mathematics ; 1726".
- catalog issued "2000".
- catalog issued "2000.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "510 s 515/.35 21".
- catalog subject "Differential equations Asymptotic theory.".
- catalog subject "Differential equations, partial.".
- catalog subject "Mathematics.".
- catalog subject "QA3.L28 no. 1726 QA372".
- catalog subject "Variational principles.".
- catalog tableOfContents "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.".
- catalog title "Regular variation and differential equations / Vojislav Marić.".
- catalog type "text".