Differential Equations with Operator Coefficients

with Applications to Boundary Value Problems for Partial Differential Equations

V. Kozlov, Vladimir Maz'Ya

442 pages, parution le 01/01/1999

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Résumé

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.

Contents

Introduction

Pt. I: Differential Equations with Constant Operator Coefficients

1: Power-Exponential Zeros
2: Differential Operator Equations in Weighted Sobolev Spaces
3: Solutions in a Local Sobolev Space
4: Two-Weight L(subscript 2)-Estimates

Pt. II: Differential Equations with Variable Operator Coefficients

5: Existence, Uniqueness and "Pointwise" Estimates
6: Corollaries of Previous Results Under Special Assumptions on L(t, D(subscript t))
7: Two-Weight L(subscript 2)-Estimates for Equations with Variable Coefficients
8: Connection of Solutions Corresponding to Different Strips
9: Applications to the Case of Perturbations Vanishing at Infinity
10: Variants and Extensions of the Previous Theory

Pt. III: Asymptotic Theory of Operator Differential Equations

11: Complete Asymptotic Expansions Under Exponential and Power Perturbations of A(D(subscript t))
12: Reduction to a First Order System
13: General Asymptotic Representation
14: Power-Exponential Asymptotics
15: The Case of One Simple Eigenvalue on the Line
16: Several Simple Eigenvalues on the Line
17: The Case of a Single Multiple Eigenvalue

A: Holomorphic Operator Functions

References
Index of Notation
Index
Index of Names

L'auteur - Vladimir Maz'Ya

Vladimir Maz'ya est Professeur à l'université Liverpool, Ohio et à l'université de Linköping.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	V. Kozlov, Vladimir Maz'Ya
Parution	01/01/1999
Nb. de pages	442
Format	16 x 24
Couverture	Relié
Poids	797g
Intérieur	Noir et Blanc
EAN13	9783540651192