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Integral Inequalities and Applications : Astrophysics and Space Science Library - D.D. Bainov

Integral Inequalities and Applications

Astrophysics and Space Science Library

Hardcover

Published: 31st May 1992
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This volume is devoted to integral inequalities of the Gronwall-Bellman-Bihari type. Following a systematic exposition of linear and nonlinear inequalities, attention is paid to analogues including integro-differential inequalities, functional differential inequalities, and discrete and abstract analogues. Applications to the investigation of the properties of solutions of various classes of equations such as uniqueness, stability, dichotomy, asymptotic equivalence and behaviour is also discussed.
The book comprises three chapters. Chapter I and II consider classical linear and nonlinear integral inequalities. Chapter III is devoted to various classes of integral inequalities of Gronwall type, and their analogues, which find applications in the theory of integro-differential equations, partial differential equations, differential equations with deviating argument, impube differential equations, etc. Each chapter concludes with a section illustrating the manner of application. The book also contains an extensive bibliography.
For researchers whose work involves the theory and application of integral inequalities in mathematics, engineering and physics.

Series Editor's Preface
Preface
Notation
Scalar linear integral inequalitiesp. 1
Gronwall-type inequalitiesp. 1
Inequalities of the type of Chu and Metcalfp. 13
Applicationsp. 16
Uniqueness of the solutionp. 17
Differentiability of the solutionp. 17
Estimate for the Cauchy matrix of a perturbed linear equationp. 18
Stability of a perturbed linear equationp. 19
Exponential and ordinary dichotomy. Asymptotic equivalence of linear equationsp. 20
Stability of the centre manifoldp. 24
Chapter I: notes and commentsp. 27
Scalar nonlinear integral inequalitiesp. 29
Integral inequalities investigated by nonstandard methodsp. 29
Bihari-type inequalitiesp. 40
Comparison resultsp. 53
Lakshmikantham's comparison methodp. 59
Inequalities of the type of Deo and Dhongadep. 67
Applicationsp. 76
Two-sided estimatesp. 76
Global existencep. 78
Terminal value problemp. 80
Stability by linear transformationp. 81
Perturbed nonlinear equationsp. 85
Chapter II: notes and commentsp. 87
Analogues of Gronwall's inequalityp. 89
Integral inequalities involving several integralsp. 89
Integral inequalities with iterated integralsp. 98
Integral inequalities for functions of N variablesp. 109
Integro-differential inequalitiesp. 133
Integral inequalities with delayp. 142
Discrete inequalitiesp. 157
Impulse integral inequalitiesp. 181
Inequalities involving Stieltjes integralsp. 191
Systems of integral inequalitiesp. 196
Inequalities in partially ordered spacesp. 201
Applicationsp. 211
Asymptotic behaviour of solutionsp. 211
Integro-differential equationsp. 213
Partial differential equationsp. 214
Functional differential equationsp. 216
Difference equationsp. 218
Impulse equationsp. 223
Chapter III: notes and commentsp. 227
Bibliographyp. 229
Author Indexp. 243
Subject Indexp. 245
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792317142
ISBN-10: 0792317149
Series: Astrophysics and Space Science Library
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 245
Published: 31st May 1992
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 1.6
Weight (kg): 0.54