Generalized inverse operators: with an introduction to Fredholm boundary-value problems

The book is devoted to the theory of generalized inverses of operators in a Banach space and its applications to linear and weakly nonlinear boundary-value problems for various classes of functional-differential equations, including systems of ordinary differential and difference equations, systems...

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Main Authors Boichuk, Alexander Andreevych, Samoilenko, Anatolii M, Malyshev, Peter V
Format eBook
LanguageEnglish
Published De Gruyter 22.08.2016
EditionSecond Edition.
SeriesInverse and ill-posed problems series
Subjects
Banach spaces
Boundary value problems
Operator theory
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ISBN3110378396
9783110378399

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Abstract The book is devoted to the theory of generalized inverses of operators in a Banach space and its applications to linear and weakly nonlinear boundary-value problems for various classes of functional-differential equations, including systems of ordinary differential and difference equations, systems of differential equations with delay, systems with impulse action, and integro-differential systems.
AbstractList The book is devoted to the theory of generalized inverses of operators in a Banach space and its applications to linear and weakly nonlinear boundary-value problems for various classes of functional-differential equations, including systems of ordinary differential and difference equations, systems of differential equations with delay, systems with impulse action, and integro-differential systems.
The book is devoted to the foundations of the theory of boundary-value problems for various classes of systems of differential-operator equations whose linear part is represented by Fredholm operators of the general form. A common point of view on numerous classes of problems that were traditionally studied independently of each other enables us to study, in a natural way, the theory of these problems, to supplement and improve the existing results, and in certain cases, study some of these problems for the first time.With the help of the technique of generalized inverse operators, the Vishik- Lyusternik method, and iterative methods, we perform a detailed investigation of the problems of existence, bifurcations, and branching of the solutions of linear and nonlinear boundary-value problems for various classes of differential-operator systems and propose new procedures for their construction.For more than 11 years that have passed since the appearance of the first edition of the monograph, numerous new publications of the authors in this direction have appeared. In this connection, it became necessary to make some additions and corrections to the previous extensively cited edition, which is still of signifi cant interest for the researchers.For researchers, teachers, post-graduate students, and students of physical and mathematical departments of universities. Contents:Preliminary InformationGeneralized Inverse Operators in Banach SpacesPseudoinverse Operators in Hilbert SpacesBoundary-Value Problems for Operator EquationsBoundary-Value Problems for Systems of Ordinary Differential EquationsImpulsive Boundary-Value Problems for Systems of Ordinary Differential EquationsSolutions of Differential and Difference Systems Bounded on the Entire Real Axis
Author Samoilenko, Anatolii M
Boichuk, Alexander Andreevych
Malyshev, Peter V
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Snippet The book is devoted to the theory of generalized inverses of operators in a Banach space and its applications to linear and weakly nonlinear boundary-value...
The book is devoted to the foundations of the theory of boundary-value problems for various classes of systems of differential-operator equations whose linear...
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SubjectTerms Banach spaces
Boundary value problems
Operator theory
Title Generalized inverse operators: with an introduction to Fredholm boundary-value problems
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