Umfang:
Online-Ressource (xi, 303 p)
Ausgabe:
Reproduktion 2011
ISBN:
9783110893014
,
3110189429
,
9783110189421
Serie:
De Gruyter Series in Nonlinear Analysis and Applications 11
Inhalt:
Biographical note: Stanislav V. Emelyanov, Nikolai A. Bobylev† and Alexander V. Bulatov, Russian Academy of Sciences, Moscow, Russia; Sergey K. Korovin, Moscow State University (Lomonosov), Moscow, Russia.
Inhalt:
This monograph provides a thorough treatment of parameter-dependent extremal problems with local minimum values that remain unchanged under changes of the parameter. The authors consider the theory as well the practical treatment of those problems, both in finite-dimensional as well as in infinite-dimensional spaces. Various applications are considered, e.g., variational calculus, control theory and bifurcations theory. Thorough treatment of parameter-dependent extremal problems with local minimum values. Includes many applications, e.g., variational calculus, control theory and bifurcations theory. Intended for specialists in the field of nonlinear analysis and its applications as well as for students specializing in these subjects.
Inhalt:
Review text: "Overall this is a book which should interest many researchers and students working on either variational problems or topological methods for nonlinear boundary value problems."James R. Ward in: Mathematical Reviews 2009b "The book is carefully written an it can be read by graduate students. Physicists and engineers who use variational methods will also find here a good source of information."In: EMS Newsletter 9/2008
Anmerkung:
Includes bibliographical references (p. [281]-292) and indexes
,
Preface; Introduction; 1 Preliminaries; 1.1 Topological, Metric, and Normed Spaces; 1.2 Compactness; 1.3 Linear Functionals and Dual Spaces; 1.4 Linear Operators; 1.5 Nonlinear Operators and Functionals; 1.6 Contraction Mappings, the Implicit Function Theorem, and Differential Equations in a Banach Space; 1.7 Minimizers of Nonlinear Functionals; 1.8 Monotonicity; 2 Finite-Dimensional Problems; 2.1 Nondegenerate Deformations of Smooth Functions; 2.2 Nondegenerate Deformations of Nonsmooth Functions; 2.3 Converses of Deformation Theorems; 2.4 Theorems of Hopf and Parusinski
,
3 Infinite-Dimensional Problems3.1Deformations of Functionals on Hilbert Spaces; 3.2 Deformations of Functionals on Banach Spaces; 3.3 Global Deformations of Functionals; 3.4 Deformations of Lipschitzian Functionals; 3.5 Deformations of Nonsmooth Problems with Constraints; 4 Conley Index; 4.1 Conley Index in Finite-Dimensional Problems; 4.2 Conley Index in Infinite-Dimensional Problems; 5 Applications; 5.1 Problems of Classical Analysis; 5.2 Nonlinear Programming Problems; 5.3 Multicriteria Problems; 5.4 Problems in the Calculus of Variations
,
5.5 Stability of Solutions of Ordinary Differential Equations5.6 Optimal Control Problems; 5.7 Bifurcation of Critical Points in Variational Problems; Additional Remarks and Bibliographic Comments; References; Notation; Name Index; Subject Index
,
In English
Weitere Ausg.:
ISBN 3110189429
Weitere Ausg.:
ISBN 9783110189421
Weitere Ausg.:
ISBN 9783110893014
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe ISBN 978-3-11-089301-4
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Homotopy of extremal problems Berlin [u.a.] : de Gruyter, 2007 ISBN 9783110189421
Weitere Ausg.:
ISBN 3110189429
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Variationsproblem
;
Einbettungsmethode
DOI:
10.1515/9783110893014
URL:
Volltext
(lizenzpflichtig)
Mehr zum Autor:
Emelʹjanov, Stanislav V. 1929-
