دانلود کتاب Nonlinear Functional Analysis - A First Course

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Preface to the Second Edition Preface to the First Edition Contents About the Author 1 Differential Calculus on Normed Linear Spaces 1.1 The Fréchet Derivative 1.2 Higher-Order Derivatives 1.3 Some Important Theorems 1.4 Extrema of Real-Valued Functions References 2 The Brouwer Degree 2.1 Definition of the Degree 2.2 Properties of the Degree 2.3 Brouwer's Theorem and Applications 2.4 Monotone Mappings on Hilbert Spaces 2.5 Borsuk's Theorem 2.6 The Genus References 3 The Leray–Schauder Degree 3.1 Preliminaries 3.2 Definition of the Degree 3.3 Properties of the Degree 3.4 Fixed Point Theorems 3.5 The Index 3.6 An Application to Differential Equations References 4 Bifurcation Theory 4.1 Introduction 4.2 The Lyapunov–Schmidt Method 4.3 Morse's Lemma 4.4 A Perturbation Method 4.5 Krasnoselsk'ii's Theorem 4.6 Rabinowitz' Theorem 4.7 A Variational Method References 5 Critical Points of Functionals 5.1 Minimization of Functionals 5.2 Saddle Points 5.3 The Palais–Smale Condition 5.4 The Deformation Lemma 5.5 The Mountain Pass Theorem 5.6 Multiplicity of Critical Points 5.7 Critical Points with Constraints References Index