Partial Integral Operators and Integro-Differential Equations: Pure and Applied Mathematics

by Jurgen Appell (Editor), Anatolij Kalitvin (Editor), Petr Zabrejko (Editor)

Overview

A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linea

Product Details

ISBN-13:	9781040214565
Publisher:	CRC Press
Publication date:	02/29/2000
Series:	Chapman & Hall/CRC Pure and Applied Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	578
File size:	736 KB

About the Author

Jurgen Appell, Anatolij Kalitvin, Petr Zabrejko

Table of Contents

Equations of Barbashin type: differential equations in Banach spaces; Barbashin equations in the space C; Barbashin equations in Lebesgue spaces; Barbashin equations in ideal spaces. Theory of linear Barbashin equations: stability of solutions; continuous dependence on parameters; bounded and periodic solutions; degenerate kernels; stationary boundary value problems; non-stationary boundary value problems; general properties; operators in spaces with mixed norm; partial integral operators in the space C; spectral properties; linear partial integral equations. Generalizations and applications: generalized equations of Barbashin type; nonlinear equations and operators; the Newton-Kantorovich method; applications of Barbashin equations; applications of partial integral equations.

Editorial Reviews

Thee authors, from Germany, Russia, and Belorussia, examine the two related notions. They describe partial integral operators as linear or nonlinear operators with integrals that depend on a parameter. The integro-differential equations are of the Barbashin type in that the right-hand sides contain both a multiplication operator and an integral operator. The connection, they explain, is that an initial value problem for a Barbashin integro-differential equation, linear or nonlinear, leads in a natural way to a fixed-point problem involving a partial integral operator. Drawing on research in Russia much of which has not even been referenced in the west, they cover first the equations of the Barbashin type and the theory behind them, then the operators. They close with generalizations and applications of each. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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