UID:
almahu_9949697613402882
Format:
1 online resource (439 p.)
ISBN:
1-281-76320-9
,
9786611763206
,
0-08-057044-5
Series Statement:
Pure and applied mathematics, a series of monographs and textbooks ; v. 74
Content:
Nonlinearity & Functional Analysis
Note:
Description based upon print version of record.
,
Front Cover; Nonlinearity and Functional Analysis: Lectures on Nonlinear Problems in Mathematical Analysis; Copyright Page; Contents; Preface; Notation and Terminology; Suggestions for The Reader; PART I: PRELIMINARIES; Chapter 1. Background Material; 1.1 How Nonlinear Problems Arise; 1.2 Typical Difficulties Encountered; 1.3 Facts from Functional Analysis; 1.4 Inequalities and Estimates; 1.5 Classical and Generalized Solutions of Differential Systems; 1.6 Mappings between Finite-Dimensional Spaces; Chapter 2. Nonlinear Operators; 2.1 Elementary Calculus; 2.2 Specific Nonlinear Operators
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2.3 Analytic Operators2.4 Compact Operators; 2.5 Gradient Mappings; 2.6 Nonlinear Fredholm Operators; 2.7 Proper Mappings; Notes; PART II: LOCAL ANALYSIS; Chapter 3. Local Analysis of a Single Mapping; 3.1 Successive Approximations; 3.2 The Steepest Descent Method for Gradient Mappings; 3.3 Analytic Operators and the Majorant Method; 3.4 Generalized Inverse Function Theorems; Notes; Chapter 4. Parameter Dependent Perturbation Phenomena; 4.1 Bifurcation Theory-A Constructive Approach; 4.2 Transcendental Methods in Bifurcation Theory; 4.3 Specific Bifurcation Phenomena
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4.4 Asymptotic Expansions and Singular Perturbations4.5 Some Singular Perturbation Problems of Classical Mathematical Physics; Notes; PART III: ANALYSIS IN THE LARGE; Chapter 5. Global Theories for General Nonlinear Operators; 5.1 Linearization; 5.2 Finite-Dimensional Approximations; 5.3 Homotopy, the Degree of Mappings, and Its Generalizations; 5.4 Homotopy and Mapping Properties of Nonlinear Operators; 5.5 Applications to Nonlinear Boundary Value Problems; Notes; Chapter 6. Critical Point Theory for Gradient Mappings; 6.1 Minimization Problems
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6.2 Specific Minimization Problems from Geometry and Physics6.3 lsoperimetric Problems; 6.4 Isoperimetric Problems in Geometry and Physics; 6.5 Critical Point Theory of Marston Morse in Hilbert Space; 6.6 The Critical Point Theory of Ljusternik and Schnirelmann; 6.7 Applications of the General Critical Point Theories; Notes; Appendix A. On Differentiable Manifolds; Appendix B. On the Hodge-Kodaira Decomposition for Differential Forms; References; Index; Pure and Applied Mathematics
,
English
Additional Edition:
ISBN 0-12-090350-4
Language:
English
