Overview

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.

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9783540651192

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Reviews

From the reviews of the first edition: <p> 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 a ] . 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)

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)

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