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Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations : MATHEMATICS AND ITS APPLICATIONS (KLUWER ACADEMIC PUB) SOVIET SERIES - I.T. Kiguradze

Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations

MATHEMATICS AND ITS APPLICATIONS (KLUWER ACADEMIC PUB) SOVIET SERIES

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Published: 30th November 1992
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This volume provides a comprehensive review of the developments which have taken place during the last thirty years concerning the asymptotic properties of solutions of nonautonomous ordinary differential equations. The conditions of oscillation of solutions are established, and some general theorems on the classification of equations according to their oscillatory properties are proved. In addition, the conditions are found under which nonlinear equations do not have singular, proper, oscillatory and monotone solutions.
The book has five chapters: Chapter I deals with linear differential equations; Chapter II with quasilinear equations; Chapter III with general nonlinear differential equations; and Chapter IV and V deal, respectively, with higher-order and second-order differential equations of the Emden-Fowler type.
Each section contains problems, including some which presently remain unsolved. The volume concludes with an extensive list of references.
For researchers and graduate students interested in the qualitative theory of differential equations.

Series Editor's preface
Preface
Basic Notation
Linear Differential Equationsp. 1
Equations Having Properties A and Bp. 1
Oscillatory and Nonoscillatory Equationsp. 42
Oscillation Properties of Solutions of Equations with Strongly Oscillating Coefficientsp. 68
The Subspace of Solutions Vanishing at Infinityp. 76
Bounded and Unbounded Solutionsp. 106
Asymptotic Formulasp. 128
Quasilinear Differential Equationsp. 145
Statement of the Problem. Auxiliary Assertionsp. 145
The Family of [actual symbol not reproducible] Type Solutions of the Equation (7.1)p. 152
[actual symbol not reproducible] Type Equationsp. 169
General Nonlinear Differential Equationsp. 179
Theorems on the Classification of Equations with Respect to Their Oscillation Propertiesp. 179
Singular Solutionsp. 198
Fast Growing Solutionsp. 207
Kneser Solutionsp. 212
Proper Oscillatory Solutionsp. 220
Higher Order Differential Equations of Emden-Fowler Typep. 235
Oscillatory Solutionsp. 235
Nonoscillatory Solutionsp. 242
Second Order Differential Equations of Emden-Fowler Typep. 249
Existence Theorems for Proper and Singular Solutionsp. 249
Oscillation and Nonoscillation Criteria for Proper Solutionsp. 256
Unbounded and Bounded Solutions. Solutions Vanishing at Infinityp. 265
Asymptotic Formulasp. 270
Referencesp. 307
Author Indexp. 329
Subject Indexp. 331
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792320593
ISBN-10: 079232059X
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER ACADEMIC PUB) SOVIET SERIES
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 331
Published: 30th November 1992
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.77 x 16.51  x 2.54
Weight (kg): 0.65