Topological Nonlinear Analysis II

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.