An introduction to nonlinear functional analysis and elliptic problems
Title Statements
- Full title :An introduction to nonlinear functional analysis and elliptic problems.
Edition Statements
- Publication Date:2011.
Publication Statements
- Publisher(s):Birkhäuser
- Place of Publication:Boston
- Language:eng
- Publication Date:2011.
The Physical Object
- Description:199 blz. ; : .. cm.
Edition Identifiers
- ISBN:9780817681135, 0817681132
- oclc:ocn840447210
- Dewey Decimal:515/.3533
Table of Contents
Machine generated contents note: 1.Preliminaries -- 1.1.Sobolev Spaces -- 1.1.1.Embedding Theorems -- 1.2.Linear Elliptic Equations -- 1.2.1.Frechet Differentiability -- 1.2.2.Nemitski Operators -- 1.2.3.Dirichlet Principle -- 1.2.4.Regularity of the Solutions -- 1.2.5.The Inverse of the Laplace Operator -- 1.3.Linear Elliptic Eigenvalue Problems -- 1.3.1.Linear Compact Operators -- 1.3.2.Variational Characterization of The Eigenvalues -- 2.Some Fixed Point Theorems -- 2.1.The Banach Contraction Principle -- 2.2.Increasing Operators -- 3.Local and Global Inversion Theorems -- 3.1.The Local Inversion Theorem -- 3.2.The Implicit Function Theorem -- 3.3.The Lyapunov-Schmidt Reduction -- 3.4.The Global Inversion Theorem -- 3.5.A Global Inversion Theorem with Singularities -- 4.Leray-Schauder Topological Degree -- 4.1.The Brouwer Degree -- 4.2.The Leray-Schauder Topological Degree -- 4.2.1.Index of an Isolated Zero and Computation by Linearization -- 4.3.Continuation Theorem of Leray-Schauder -- 4.3.1.A Topological Lemma -- 4.3.2.A Theorem by Leray and Schauder -- 4.4.Other Continuation Theorems -- 5.An Outline of Critical Points -- 5.1.Definitions -- 5.2.Minima -- 5.3.The Mountain Pas…
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