Ebook: Topological Nonlinear Analysis II: Degree, Singularity and Variations
- Tags: Topology, Global Analysis and Analysis on Manifolds, Analysis
- Series: Progress in Nonlinear Differential Equations and Their Applications 27
- Year: 1996
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-ix
Classical Solutions for a Perturbed N-Body System....Pages 1-86
Degree Theory: Old and New....Pages 87-108
Global Structure for Nonlinear Operators in Differential and Integral Equations I. Folds....Pages 109-160
Global Structure for Nonlinear Operators in Differential and Integral Equations II. Cusps....Pages 161-245
Degree for Gradient Equivariant Maps and Equivariant Conley Index....Pages 247-272
Variations and Irregularities....Pages 273-313
Singularity Theory and Bifurcation Phenomena in Differential Equations....Pages 315-395
Bifurcation from the Essential Spectrum....Pages 397-443
Rotation of Vector Fields: Definition, Basic Properties, and Calculation....Pages 445-601
Back Matter....Pages 603-605
Content:
Front Matter....Pages i-ix
Classical Solutions for a Perturbed N-Body System....Pages 1-86
Degree Theory: Old and New....Pages 87-108
Global Structure for Nonlinear Operators in Differential and Integral Equations I. Folds....Pages 109-160
Global Structure for Nonlinear Operators in Differential and Integral Equations II. Cusps....Pages 161-245
Degree for Gradient Equivariant Maps and Equivariant Conley Index....Pages 247-272
Variations and Irregularities....Pages 273-313
Singularity Theory and Bifurcation Phenomena in Differential Equations....Pages 315-395
Bifurcation from the Essential Spectrum....Pages 397-443
Rotation of Vector Fields: Definition, Basic Properties, and Calculation....Pages 445-601
Back Matter....Pages 603-605
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