Eberhard Zeidler

Nonlinear Functional Analysis and its Applications

I: Fixed-Point Theorems
Übersetzung:Wadsack, P.R.

• Broschiertes Buch

Produktbeschreibung

The greatest mathematicians, such as Archimedes, Newton, and Gauss, always united theory and applications in equal measure. Felix Klein There exists the remarkable possibility that one can master a subject mathemati cally, without really understanding its essence. Albert Einstein Don't give us numbers: give us insight! A contemporary natural scientist to a mathematician Numerous questions in physics, chemistry, biology, and economics lead to nonlinear problems; for example, deformation of rods, plates, and shells; behavior of plastic materials; surface waves of fluids; flows around objects in fluids or gases; shock waves in gases; movement of viscous fluids; equilibrium forms of rotating fluids in astrophysics; determination of the shape of the earth through gravitational measu- ments; behavior of magnetic fields of astrophysical objects; melting processes; chemical reactions; heat radiation; processes in nuclear reactors; nonlinear oscillation in physics, chemistry, and biology;2 Introduction existence and stability of periodic and quasiperiodic orbits in celestial mechanics; stability of physical, chemical, biological, ecological, and economic processes; diffusion processes in physics, chemistry, and biology; processes with entropy production, and self-organization of systems in physics, chemistry, and biology; study of the electrical potential variation in the heart through measure ments on the body surface to prevent heart attacks; determining material constants or material laws (e. g.

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Produktdetails

• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4612-9323-1
• 1986
• Seitenzahl: 936
• Erscheinungstermin: 14. Oktober 2011
• Englisch
• Abmessung: 235mm x 155mm x 50mm
• Gewicht: 1407g
• ISBN-13: 9781461293231
• ISBN-10: 1461293235
• Artikelnr.: 40773019

Autorenporträt

Prof. Dr. Dr. h.c. Eberhard Zeidler works at the Max Planck Institute for Mathematics in the Sciences in Leipzig (Germany). In 1996 he was one of the founding directors of this institute. He is a member of the Academy of Natural Scientists Leopoldina. In 2006 he was awarded the 'Alfried Krupp Wissenschaftspreis' of the Alfried Krupp von Bohlen und Halbach-Stiftung.

Inhaltsangabe

Fundamental Fixed-Point Principles.- 1 The Banach Fixed-Point Theorem and Iterative Methods.- 2 The Schauder Fixed-Point Theorem and Compactness.- Applications of the Fundamental Fixed-Point Principles.- 3 Ordinary Differential Equations in B-spaces.- 4 Differential Calculus and the Implicit Function Theorem.- 5 Newton's Method.- 6 Continuation with Respect to a Parameter.- 7 Positive Operators.- 8 Analytic Bifurcation Theory.- 9 Fixed Points of Multivalued Maps.- 10 Nonexpansive Operators and Iterative Methods.- 11 Condensing Maps and the Bourbaki-Kneser Fixed-Point Theorem.- The Mapping Degree and the Fixed-Point Index.- 12 The Leray-Schauder Fixed-Point Index.- 13 Applications of the Fixed-Point Index.- 14 The Fixed-Point Index of Differentiable and Analytic Maps.- 15 Topological Bifurcation Theory.- 16 Essential Mappings and the Borsuk Antipodal Theorem.- 17 Asymptotic Fixed-Point Theorems.- References.- Additional References to the Second Printing.- List of Symbols.- List of Theorems.- List of the Most Important Definitions.- Schematic Overviews.- General References to the Literature.- List of Important Principles.- of the Other Parts.

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Fundamental Fixed
Point Principles.
1 The Banach Fixed
Point Theorem and Iterative Methods.
2 The Schauder Fixed
Point Theorem and Compactness.
Applications of the Fundamental Fixed
Point Principles.
3 Ordinary Differential Equations in B
spaces.
4 Differential Calculus and the Implicit Function Theorem.
5 Newton's Method.
6 Continuation with Respect to a Parameter.
7 Positive Operators.
8 Analytic Bifurcation Theory.
9 Fixed Points of Multivalued Maps.
10 Nonexpansive Operators and Iterative Methods.
11 Condensing Maps and the Bourbaki
Kneser Fixed
Point Theorem.
The Mapping Degree and the Fixed
Point Index.
12 The Leray
Schauder Fixed
Point Index.
13 Applications of the Fixed
Point Index.
14 The Fixed
Point Index of Differentiable and Analytic Maps.
15 Topological Bifurcation Theory.
16 Essential Mappings and the Borsuk Antipodal Theorem.
17 Asymptotic Fixed
Point Theorems.
References.
Additional References to the Second Printing.
List of Symbols.
List of Theorems.
List of the Most Important Definitions.
Schematic Overviews.
General References to the Literature.
List of Important Principles.
of the Other Parts.