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Differential Equations with Operator Coefficients : With Applications to Boundary Value Problems for Partial Differential Equations :  With Applications to Boundary Value Problems for Partial Differential Equations - V. V. Kozlov

Differential Equations with Operator Coefficients : With Applications to Boundary Value Problems for Partial Differential Equations

With Applications to Boundary Value Problems for Partial Differential Equations

Hardcover

Published: July 2009
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This book is the first systematic and self-contained presentation of a theory of arbitrary order ordinary differential equations with unbounded operator coefficients in a Hilbert or Banach space, developed over the last 10 years by the authors. It deals with conditions of solvability, classes of uniqueness, estimates for solutions and asymptotic representations of solutions at infinity. The authors show how the classical asymptotic theory of ODEs. with scalar coefficients can be extended to very general equations with unbounded operator coefficients. In contrast to other works the authors' approach enables them to obtain asymptotic formulae for solutions under weak conditions on the coefficients of equations. The abstract results are complemented by many new applications to the theory of PDEs. An appendix provides a systematic treatment of the theory of holomorphic operator functions.

From the reviews of the first edition:





"The book under review is the first systematic and self-contained presentation of a theory of arbitrary order ordinary differential equations with unbounded operator coefficients in a Hilbert or Banach space ... . this is an excellent book, that contains recent results of the topic, deep theoretical results and various applications to PDE-s. It is warmly recommended to specialists in ODE-s, PDE-s, functional analysis." (Jeno Hegedus, Acta Scientiarum Mathematicarum, Vol. 72, 2006)

Introduction
Differential Equations with Constant Operator Coefficients
Power-Exponential Zerosp. 3
Differential Operator Equations in Weighted Sobolev Spacesp. 27
Solutions in a Local Sobolev Spacep. 49
Two-Weight L[subscript 2]-Estimatesp. 75
Differential Equations with Variable Operator Coefficients
Existence, Uniqueness and "Pointwise" Estimatesp. 91
Corollaries of Previous Results Under Special Assumptions on L(t, D[subscript t])p. 113
Two-Weight L[subscript 2]-Estimates for Equations with Variable Coefficientsp. 133
Connection of Solutions Corresponding to Different Stripsp. 147
Applications to the Case of Perturbations Vanishing at Infinityp. 165
Variants and Extensions of the Previous Theoryp. 181
Asymptotic Theory of Operator Differential Equations
Complete Asymptotic Expansions Under Exponential and Power Perturbations of A(D[subscript t])p. 245
Reduction to a First Order Systemp. 265
General Asymptotic Representationp. 285
Power-Exponential Asymptoticsp. 317
The Case of One Simple Eigenvalue on the Linep. 345
Several Simple Eigenvalues on the Linep. 369
The Case of a Single Multiple Eigenvaluep. 385
Holomorphic Operator Functionsp. 403
Referencesp. 431
Index of Notationp. 435
Indexp. 439
Index of Namesp. 441
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540651192
ISBN-10: 3540651195
Series: Springer Monographs in Mathematics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 444
Published: July 2009
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 3.18
Weight (kg): 1.83