Title | Topological Nonlinear Analysis II [electronic resource] : Degree, Singularity and Variations / edited by Michele Matzeu, Alfonso Vignoli |
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Imprint | Boston, MA : Birkhรคuser Boston, 1997 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4126-3 |
Descript | X, 605 p. online resource |
Classical Solutions for a Perturbed N-Body System -- Variational Setting for Newtonโs 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 -- Frรฉchet Derivatives -- Fredholm Maps -- Local Structure of Folds -- Abstract Global Characterization of the Fold Map -- Ambrosetti-Prodi and Berger-Podolak โ 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 Kรกrmรกn 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 โ Initial Results -- u3 Dirichlet Map โ The Singular Set and its Image -- u3 Dirichlet Map โ The Global Result -- Ruf u3 Neumann Cusp Map -- Rufโs Higher Order Singularities -- Damonโs 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