
Generalized Inverse Operators and Fredholm Boundary-Value Problems
VSP International Science Publishers
1st Edition
Published on 31. March 2004
Book
Hardback
317 pages
978-90-6764-407-5 (ISBN)
Article exhausted; check different version
Description
01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information.
The problems of development of constructive methods for the analysis of linear and weakly nonlinear boundary-value problems for a broad class of functional differential equations traditionally occupy one of the central places in the qualitative theory of differential equations.
The authors of this monograph suggest some methods for the construction of the generalized inverse (or pseudo-inverse) operators for the original linear Fredholm operators in Banach (or Hilbert) spaces for boundary-value problems regarded as operator systems in abstract spaces. They also study basic properties of the generalized Green's operator.
In the first three chapters some results from the theory of generalized inversion of bounded linear operators in abstract spaces are given, which are then used for the investigation of boundary-value problems for systems of functional differential equations. Subsequent chapters deal with a unified procedure for the investigation of Fredholm boundary-value problems for operator equations; analysis of boundary-value problems for standard operator systems; and existence of solutions of linear and nonlinear differential and difference systems bounded on the entire axis.
The problems of development of constructive methods for the analysis of linear and weakly nonlinear boundary-value problems for a broad class of functional differential equations traditionally occupy one of the central places in the qualitative theory of differential equations.
The authors of this monograph suggest some methods for the construction of the generalized inverse (or pseudo-inverse) operators for the original linear Fredholm operators in Banach (or Hilbert) spaces for boundary-value problems regarded as operator systems in abstract spaces. They also study basic properties of the generalized Green's operator.
In the first three chapters some results from the theory of generalized inversion of bounded linear operators in abstract spaces are given, which are then used for the investigation of boundary-value problems for systems of functional differential equations. Subsequent chapters deal with a unified procedure for the investigation of Fredholm boundary-value problems for operator equations; analysis of boundary-value problems for standard operator systems; and existence of solutions of linear and nonlinear differential and difference systems bounded on the entire axis.
Reviews / Votes
'The book is devoted to the theory of generalized inverses of operators in a Banch space and its applications to linear and wealy nonlinear boundary-value problems for various classes of functional-differential equations, including systems of ordinary differential and difference equitions, systems of differential equations with delay, systems with impulse action, and integro-differential systems.'Michael I. Gil, Mathematical Reviews, 2006.
More details
Language
English
Place of publication
Zeist
Netherlands
Publishing group
Brill
Target group
Professional and scholarly
This book will be of value and interest to anyone working in the fields of differential equations and nonlinear oscillations.
Product notice
Laminated cover
Weight
650 gr
ISBN-13
978-90-6764-407-5 (9789067644075)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
A. A. Boichuk | Anatolii M. Samoilenko
Generalized Inverse Operators and Fredholm Boundary-Value Problems
Book
01/2004
1st Edition
De Gruyter
€359.00
Article exhausted; check different version
Content
Frontmatter
Contents
NOTATION
PREFACE
1. PRELIMINARY INFORMATION
2. GENERALIZED INVERSE OPERATORS IN BANACH SPACES
3. PSEUDOINVERSE OPERATORS IN HILBERT SPACES
4. BOUNDARY-VALUE PROBLEMS FOR OPERATOR EQUATIONS
5. BOUNDARY-VALUE PROBLEMS FOR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
6. IMPULSIVE BOUNDARY-VALUE PROBLEMS FOR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
7. SOLUTIONS OF DIFFERENTIAL AND DIFFERENCE SYSTEMS BOUNDED ON THE ENTIRE REAL AXIS
References
Contents
NOTATION
PREFACE
1. PRELIMINARY INFORMATION
2. GENERALIZED INVERSE OPERATORS IN BANACH SPACES
3. PSEUDOINVERSE OPERATORS IN HILBERT SPACES
4. BOUNDARY-VALUE PROBLEMS FOR OPERATOR EQUATIONS
5. BOUNDARY-VALUE PROBLEMS FOR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
6. IMPULSIVE BOUNDARY-VALUE PROBLEMS FOR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
7. SOLUTIONS OF DIFFERENTIAL AND DIFFERENCE SYSTEMS BOUNDED ON THE ENTIRE REAL AXIS
References