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Volterra Integral and Functional Equations

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Hardcover | 4 June 1990

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Hardcover
724 Pages

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23.39 x 15.6 x 3.81

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The rapid development of the theories of Volterra integral and functional equations has been strongly promoted by their applications in physics, engineering and biology. This text shows that the theory of Volterra equations exhibits a rich variety of features not present in the theory of ordinary differential equations. The book is divided into three parts. The first considers linear theory and the second deals with quasilinear equations and existence problems for nonlinear equations, giving some general asymptotic results. Part III is devoted to frequency domain methods in the study of nonlinear equations. The entire text analyses n-dimensional rather than scalar equations, giving greater generality and wider applicability and facilitating generalisations to infinite-dimensional spaces. The book is generally self contained and assumes only a basic knowledge of analysis. The many exercises illustrate the development of the theory and its applications, making this book accessible to researchers in all areas of integral and differential equations.

Industry Reviews

"...an excellent encyclopedia of results on the theory of Volterra integral equations." Mathematical Reviews "Efforts have been made to cover aspects of analysis needed but not easily found elsewhere...and care is given to including an extensive table of symbols and their meaning; it is nicely produced." The Mathematical Association of America

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Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Probability & Statistics

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Paperback

Published: 19th March 2009

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Preface
List of symbols
Introduction and overview
Linear Theory
Linear convolution integral equations
Linear integro-differential convolution equations
Equations in weighted spaces
Completely monotone kernels
Nonintegrable kernels with integrable resolvents
Unbounded and unstable solutions
Volterra equations as semigroups
Linear nonconvolution equations
Linear nonconvolution equations with measure kernels
General Nonlinear Theory
Perturbed linear equations
Existence of solutions of nonlinear equations
Continuous dependence, differentiability, and uniqueness
Liapunov techniques
General asymptotics
Frequency Domain and Monotonicity Techniques
Convolution kernels of positive type
Frequency domain methods: basic results
Frequency domain methods: additional results
Combined Liapunov and frequency domain methods
Monotonicity methods
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

Volterra Integral and Functional Equations

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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