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

✍ Scribed by Vladimir Kozlov, Vladimir Maz’ya (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1999
• Tongue: English
• Leaves: 449
• Series: Springer Monographs in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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)

✦ Table of Contents

Front Matter....Pages I-XX
Front Matter....Pages 1-1
Power-Exponential Zeros....Pages 3-25
Differential Operator Equations in Weighted Sobolev Spaces....Pages 27-48
Solutions in a Local Sobolev Space....Pages 49-74
Two-Weight L 2 -Estimates....Pages 75-87
Front Matter....Pages 89-89
Existence, Uniqueness and “Pointwise” Estimates....Pages 91-112
Corollaries of Previous Results Under Special Assumptions on L ( t , D t )....Pages 113-131
Two-Weight L 2 -Estimates for Equations with Variable Coefficients....Pages 133-146
Connection of Solutions Corresponding to Different Strips....Pages 147-164
Applications to the Case of Perturbations Vanishing at Infinity....Pages 165-180
Variants and Extensions of the Previous Theory....Pages 181-241
Front Matter....Pages 243-243
Complete Asymptotic Expansions Under Exponential and Power Perturbations of A ( D t )....Pages 245-263
Reduction to a First Order System....Pages 265-283
General Asymptotic Representation....Pages 285-315
Power-Exponential Asymptotics....Pages 317-344
The Case of One Simple Eigenvalue on the Line....Pages 345-367
Several Simple Eigenvalues on the Line....Pages 369-383
The Case of a Single Multiple Eigenvalue....Pages 385-402
Back Matter....Pages 403-443

✦ Subjects

Ordinary Differential Equations