The Resource Topological Nonlinear Analysis II : Degree, Singularity and variations, by Michele Matzeu, Alfonso Vignoli, (electronic resource)

Topological Nonlinear Analysis II : Degree, Singularity and variations, by Michele Matzeu, Alfonso Vignoli, (electronic resource)

Label
Topological Nonlinear Analysis II : Degree, Singularity and variations
Title
Topological Nonlinear Analysis II
Title remainder
Degree, Singularity and variations
Statement of responsibility
by Michele Matzeu, Alfonso Vignoli
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in nonlin­ ear analysis during the last three decades. It is intended, at least partly, as a continuation of Topological Nonlinear Analysis: Degree, Singularity and Varia­ tions, published in 1995. The survey articles presented are concerned with three main streams of research, that is topological degree, singularity theory and variational methods, They reflect the personal taste of the authors, all of them well known and distinguished specialists. A common feature of these articles is to start with a historical introduction and conclude with recent results, giving a dynamic picture of the state of the art on these topics. Let us mention the fact that most of the materials in this book were pre­ sented by the authors at the "Second Topological Analysis Workshop on Degree, Singularity and Variations: Developments of the Last 25 Years," held in June 1995 at Villa Tuscolana, Frascati, near Rome. Michele Matzeu Alfonso Vignoli Editors Topological Nonlinear Analysis II Degree, Singularity and Variations Classical Solutions for a Perturbed N-Body System Gianfausto Dell 'A ntonio O. Introduction In this review I shall consider the perturbed N-body system, i.e., a system composed of N point bodies of masses ml, ... mN, described in cartesian co­ ordinates by the system of equations (0.1) where f) V'k,m == -£l--' m = 1, 2, 3
Member of
http://library.link/vocab/creatorName
Matzeu, Michele
Dewey number
514
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • lSUOF8MzUeA
  • vqldWA6PP9I
Image bit depth
0
Language note
English
LC call number
QA611-614.97
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorDate
1995
http://library.link/vocab/relatedWorkOrContributorName
  • Topological Analysis Workshop on Degree, Singularity and Variations
  • Vignoli, Alfonso.
Series statement
Progress in Nonlinear Differential Equations and Their Applications,
Series volume
27
http://library.link/vocab/subjectName
  • Topology
  • Global analysis
  • Global analysis (Mathematics)
  • Topology
  • Global Analysis and Analysis on Manifolds
  • Analysis
Label
Topological Nonlinear Analysis II : Degree, Singularity and variations, by Michele Matzeu, Alfonso Vignoli, (electronic resource)
Instantiates
Publication
Note
Papers presented at the Second Topological Analysis Workshop on Degree, Singularity and Variations, held June 1995 at Villa Tuscolana, Frascati
Antecedent source
mixed
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Classical Solutions for a Perturbed N-Body System -- Variational Setting for Newton’s Equations -- The Kepler Problem Revisited -- The N-Body Problem -- Results form Critical Point Theory -- Classical Periodic Solutions for the Perturbed N-Body System -- Acknowledgments -- References -- Degree Theory: Old and New -- Degree Theory for Maps in the Sobolev Class H1(S2, S2) -- Degree Theory for Maps in the Sobolev Class H1(S1, S1) -- Degree Theory for Maps in VMO (Sn, Sn) -- Further Properties of VMO Maps in Connection with Topology -- Degree Theory for VMO Maps on Domains -- References -- Global Structure for Nonlinear Operators in Differential and Integral Equations I. Folds -- Fréchet Derivatives -- Fredholm Maps -- Local Structure of Folds -- Abstract Global Characterization of the Fold Map -- Ambrosetti-Prodi and Berger-Podolak — Church Fold Maps -- McKean-Scovel Fold Map -- Giannoni-Micheletti Fold Map -- Mandhyan Fold Map -- Oriented Global Fold Maps -- A Second Mandhyan Fold Map -- Jumping Singularities -- References -- Global Structure for Nonlinear Operators in Differential and Integral Equations II. Cusps -- Critical Values of Fredholm Maps -- Applications of Critical Values to Nonlinear Differential Equations -- Factorization of Differentiate Maps -- Local Structure of Cusps -- Some Local Cusp Results -- von Kármán Equations -- Abstract Global Characterization of the Cusp Map -- Mandhyan Integral Operator Cusp Map -- Pseudo-Cusp -- Cafagna and Donati Theorems on Ordinary Differential Equations -- Micheletti Cusp-like Map -- Cafagna Dirichlet Example -- u3 Dirichlet Map — Initial Results -- u3 Dirichlet Map — The Singular Set and its Image -- u3 Dirichlet Map — The Global Result -- Ruf u3 Neumann Cusp Map -- Ruf’s Higher Order Singularities -- Damon’s Work in Differential Equations -- References -- Degree for Gradient Equivariant Maps and Equivariant Conley Index -- Basic Notions of Equivariant Topology -- Remarks and Examples -- An Analytic Definition of the Gradient Equivariant Degree -- Technicalities -- Equivariant Conley Index -- Box-like Index Pairs -- The torn Dieck Ring -- Bifurcation -- References -- Variations and Irregularities -- Summary -- Generalized Differential Operators -- Irregularities -- Mass, Length, Energy -- Homogeneous Dirichlet Spaces -- Fractals -- References -- Singularity Theory and Bifurcation Phenomena in Differential Equations -- The Normal Forms for f : ?n ? ?m -- The Malgrange Preparation Theorem -- Singularity Theory for Mappings Between Banach Spaces -- Applications to Elliptic Boundary Value Problems -- First Order Differential Equations -- Global Equivalence Theorems -- Problems with Additional Parameters: Unfoldings -- Bifurcation of Minimal Surfaces -- Singularities at Double Eigenvalues -- Multiplicity by combining Local and Global Information -- Some Numerical Results -- References -- Bifurcation from the Essential Spectrum -- General Setting -- Nonlinear Perturbation of a Self-Adjoint Operator -- Bifurcation from the Infimum of the Spectrum -- Bifurcation into Spectral Gaps -- Semilinear Elliptic Equations -- References -- Rotation of Vector Fields: Definition, Basic Properties, and Calculation -- The Brouwer-Hopf Theory of Continuous Vector Fields -- The Leray-Schauder Theory of Completely Continuous Vector Fields -- Vector Fields with Noncompact Operators -- Some Generalizations and Modifications -- References
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (X, 605 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461241263
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-4126-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000090715
  • (SSID)ssj0001298801
  • (PQKBManifestationID)11837362
  • (PQKBTitleCode)TC0001298801
  • (PQKBWorkID)11260032
  • (PQKB)10196406
  • (DE-He213)978-1-4612-4126-3
  • (MiAaPQ)EBC3076573
  • (EXLCZ)993400000000090715
Label
Topological Nonlinear Analysis II : Degree, Singularity and variations, by Michele Matzeu, Alfonso Vignoli, (electronic resource)
Publication
Note
Papers presented at the Second Topological Analysis Workshop on Degree, Singularity and Variations, held June 1995 at Villa Tuscolana, Frascati
Antecedent source
mixed
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Classical Solutions for a Perturbed N-Body System -- Variational Setting for Newton’s Equations -- The Kepler Problem Revisited -- The N-Body Problem -- Results form Critical Point Theory -- Classical Periodic Solutions for the Perturbed N-Body System -- Acknowledgments -- References -- Degree Theory: Old and New -- Degree Theory for Maps in the Sobolev Class H1(S2, S2) -- Degree Theory for Maps in the Sobolev Class H1(S1, S1) -- Degree Theory for Maps in VMO (Sn, Sn) -- Further Properties of VMO Maps in Connection with Topology -- Degree Theory for VMO Maps on Domains -- References -- Global Structure for Nonlinear Operators in Differential and Integral Equations I. Folds -- Fréchet Derivatives -- Fredholm Maps -- Local Structure of Folds -- Abstract Global Characterization of the Fold Map -- Ambrosetti-Prodi and Berger-Podolak — Church Fold Maps -- McKean-Scovel Fold Map -- Giannoni-Micheletti Fold Map -- Mandhyan Fold Map -- Oriented Global Fold Maps -- A Second Mandhyan Fold Map -- Jumping Singularities -- References -- Global Structure for Nonlinear Operators in Differential and Integral Equations II. Cusps -- Critical Values of Fredholm Maps -- Applications of Critical Values to Nonlinear Differential Equations -- Factorization of Differentiate Maps -- Local Structure of Cusps -- Some Local Cusp Results -- von Kármán Equations -- Abstract Global Characterization of the Cusp Map -- Mandhyan Integral Operator Cusp Map -- Pseudo-Cusp -- Cafagna and Donati Theorems on Ordinary Differential Equations -- Micheletti Cusp-like Map -- Cafagna Dirichlet Example -- u3 Dirichlet Map — Initial Results -- u3 Dirichlet Map — The Singular Set and its Image -- u3 Dirichlet Map — The Global Result -- Ruf u3 Neumann Cusp Map -- Ruf’s Higher Order Singularities -- Damon’s Work in Differential Equations -- References -- Degree for Gradient Equivariant Maps and Equivariant Conley Index -- Basic Notions of Equivariant Topology -- Remarks and Examples -- An Analytic Definition of the Gradient Equivariant Degree -- Technicalities -- Equivariant Conley Index -- Box-like Index Pairs -- The torn Dieck Ring -- Bifurcation -- References -- Variations and Irregularities -- Summary -- Generalized Differential Operators -- Irregularities -- Mass, Length, Energy -- Homogeneous Dirichlet Spaces -- Fractals -- References -- Singularity Theory and Bifurcation Phenomena in Differential Equations -- The Normal Forms for f : ?n ? ?m -- The Malgrange Preparation Theorem -- Singularity Theory for Mappings Between Banach Spaces -- Applications to Elliptic Boundary Value Problems -- First Order Differential Equations -- Global Equivalence Theorems -- Problems with Additional Parameters: Unfoldings -- Bifurcation of Minimal Surfaces -- Singularities at Double Eigenvalues -- Multiplicity by combining Local and Global Information -- Some Numerical Results -- References -- Bifurcation from the Essential Spectrum -- General Setting -- Nonlinear Perturbation of a Self-Adjoint Operator -- Bifurcation from the Infimum of the Spectrum -- Bifurcation into Spectral Gaps -- Semilinear Elliptic Equations -- References -- Rotation of Vector Fields: Definition, Basic Properties, and Calculation -- The Brouwer-Hopf Theory of Continuous Vector Fields -- The Leray-Schauder Theory of Completely Continuous Vector Fields -- Vector Fields with Noncompact Operators -- Some Generalizations and Modifications -- References
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (X, 605 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461241263
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-4126-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000090715
  • (SSID)ssj0001298801
  • (PQKBManifestationID)11837362
  • (PQKBTitleCode)TC0001298801
  • (PQKBWorkID)11260032
  • (PQKB)10196406
  • (DE-He213)978-1-4612-4126-3
  • (MiAaPQ)EBC3076573
  • (EXLCZ)993400000000090715

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