Nonlinearity & Functional Analysis : Lectures on Nonlinear Problems in Mathematical Analysis /: Lectures on Nonlinear Problems in Mathematical Analysis. ([1977?])

• Record Type: Book
• Further Information: Note: Melvyn S. Berger.
• Authors: Berger, Melvyn S
• 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; ; Notes; ; Chapter 2 Nonlinear Operators; ; 2.1 Elementary Calculus; ; 2.2 Specific Nonlinear Operators; ; 2.3 Analytic Operators; ; 2.4 Compact Operators; ; 2.5 Gradient Mappings; ; 2.6 Nonlinear Fredholrn 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; ; 4.4 Asymptotic Expansions and Singular Perturbations; ; 4.5 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; ; 6.2 Specific Minimization Problems from Geometry and Physics; ; 6.3 Isoperimetric Problems; ; 6.4 Isoperimetric Problems in Geometry and Physics; ; 6.5 Critical Point Theory of Marston Morse in Hilbert Space; ; 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;
• Publisher Details: New York : Academic press
• Publication Date: 1977
• Extent: 1 online resource, illustrations
• Subjects: 515.7; Mathematical analysis; Functional analysis; Nonlinear theories
• Languages: English
• ISBNs: 9780080570440; 0080570445
• Related ISBNs: 9780120903504; 0120903504
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.