UID:
almahu_9947366516002882
Umfang:
1 online resource (375 p.)
ISBN:
1-282-28966-7
,
9786612289668
,
0-08-095614-9
Serie:
Mathematics in science and engineering ; v. 105
Inhalt:
Introduction to the theory and application of differential equations with deviating arguments
Anmerkung:
Description based upon print version of record.
,
Front Cover; Introduction to the Theory and Application of Differential Equations with Deviating Arguments; Copyright Page; Contents; PREFACE; TRANSLATOR'S NOTE; INTRODUCTION; Chapter I. Basic Concepts and Existence Theorems; 1. Statement of the Basic Initial Value Problem. Classifications; 2. The Method of Steps; 3. Integrable Types of Equations with a Deviating Argument; 4. Existence and Uniqueness Theorems for the Solution of the Basic Initial Value Problem; 5. Some Specific Singularities of the Solutions of Equations with a Deviating Argument; Chapter II. Linear Equations
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1. Some Properties of Linear Equations2. Linear Equations with Constant Coefficients and Constant Deviating Arguments; 3. The Characteristic Quasipolynomial; 4. The Expansion of the Solution into a Series of Basic Solutions; 5. Two-Sided Solutions; 6. The Homogeneous Initial Value Problem; 7. Some Types of Linear Equations with Variable Coefficients and Variable Deviating Arguments; Chapter III. Stability Theory; 1. Basic Concepts; 2. The Stability of Solutions to Stationary Linear Equations; 3. Conditions for Negativity of the Real Parts of All Roots of the Quasipolynomial
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4. The Case of Small Deviating Arguments5. The Case of Large Deviating Arguments; 6. Lyapunov's Second Method; 7. Stability in the First Approximation; 8. Stability under Constantly Acting Disturbances; 9. Lyapunov's Second Method for Equations of Neutral Type; 10. Absolute Stability; Chapter IV. Periodic Solutions; 1. Some Properties of Periodic Solutions and Existence Theorems; 2. Periodic Solutions of Stationary, Linear, Homogeneous Equations; 3. Periodic Solutions of Linear Inhomogeneous Equations with Stationary Homogeneous Parts
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4. Periodic Solutions of Linear Equations with Variable Coefficients and Deviating Arguments5. Periodic Solutionsof Quasilinear Equations; 6. Functionally Equivalent Systems of Differential Equations with a Deviating Argument; Chapter V. Stochastic Differential Equations with a Retarded Argument; 1. Basic Concepts; 2. Stability; 3. Stationary Solutions of Equations with a Delay; Chapter VI. Approximate Methods for the Integration of Differential Equations with a Deviating Argument; 1. General Remarks about the Application of Approximate Integration Methods
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2. Euler's Method and Parabolic Methods3. Expansion in Powers of the Retardation; 4. Asymptotic Methods for Equations with Small Deviating Argument; 5. Iterative Methods; Chapter VII. Some Generalizations and a Brief Survey of Work in Other Areas of the Theory of Differential Equations with a Deviating Argument; 1. Some Generalizations; 2. Periodic Solutions; 3. Boundary-Value Problems; 4. Optimal Processes with a Retardation; 5. Stationary Points; BIBLIOGRAPHY; I. Monographs; II. Survey Articles; III. Journal Articles
,
English
Weitere Ausg.:
ISBN 0-12-237750-8
Sprache:
Englisch
