Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations

By: Ivan Kiguradze, T.A. Chanturia

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Hardcover | 30 November 1992

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Hardcover
352 Pages

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23.39 x 15.6 x 2.06

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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.

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

Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations

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Hardcover

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You Can Find This Book In

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