Lectures in Nonlinear Functional Analysis

图书简介

This book is a systematic presentation of basic notions, facts, and ideas of nonlinear functional analysis and their applications to nonlinear partial differential equations. It begins from a brief introduction to linear functional analysis, including various types of convergence and functional spaces. The main part of the book is devoted to the theory of nonlinear operators. Various methods of the study of nonlinear differential equations based on the facts of nonlinear analysis are presented in detail. This book may serve as an introductory textbook for students and undergraduates specializing in modern mathematical physics.Key Features: oIn this book, the most famous methods of nonlinear analysis and its applications scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference bookoThe presentation of the material is closed and accompanied by a large number of examples; this makes it easier to understand the material and руДЫ beginners to quickly enter into the circle of ideas discussed

Functional Analysis: Preliminaries: Linear Operators; Weak and *-Weak Convergence; Bochner Integral; Spaces of B-Valued Functions and Distributions; Nonlinear Operators: Continuity, Differentiability, and Compactness: Nonlinear Operators; Nemytsky Operator; Frechet Derivatives of Implicit Functionals in Control Theory; Compact, Completely Continuous, and Totally Continuous Operators; Local Invertibility Theorem; Variational Methods of the Study of Nonlinear Operators: Potential Operators; Semicontinuous and Coercive Functionals; L A Lyusternik’s Theorem on Conditional Extrema; S I Pokhozhaev’s Method of Spherical Fibering; M A Krasnosel’sky’s Theory of the Genus of a Set; Auxiliary Resilts; Applications of M A Krasnosel’sky’s Theory of the Genus of a Set; Methods of Monotonicity and Compactness: Galerkin Method and Method of Monotonicity Elliptic Equations; Method of Monotonic Operators General Results; Properties of the p-Laplacian; Galerkin Method and Method of Compactness Parabolic Equations, I; Galerkin Method and Method of Compactness Parabolic Equations, II; Galerkin Method and Method of Compactness Hyperbolic Equations; Methods Based on the Maximum Principle: Method of Upper and Lower Solutions for Elliptic Equations; Method of Upper and Lower Solutions for Parabolic Equations; Method of Upper and Lower Weak Solutions; Schauder Principle and Contraction Mapping Theorem: Topological Schauder Principle; Picard Theorem: Simplest Case; Theorem on Nonextendable Solutions of Cauchy Problems; Benjamin-Bona-Mahony-Burgers Equation; Examples of Global Solvability; Various Generalizations and Limits of Applicability; Bibliography;

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Lectures in Nonlinear Functional Analysis 非线性泛函分析讲座：莫斯科国立罗蒙诺索夫大学物理系讲座概要超群理论 泛函分析

Lectures in Nonlinear Functional Analysis

非线性泛函分析讲座：莫斯科国立罗蒙诺索夫大学物理系讲座概要超群理论
泛函分析