Variational Methods in Nonlinear Analysis: With Applications in Optimization and Partial Differential Equations

✍ Scribed by Dimitrios C. Kravvaritis; Athanasios N. Yannacopoulos

Publisher: De Gruyter
Year: 2020
Tongue: English
Leaves: 500
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.

A pedagogical presentation of nonlinear analysis at the graduate level
Puts a focus on variational techniques and their numerous applications
Of interest to graduate students, lecturers, and researchers

✦ Table of Contents

Preface
Contents
Notation
1 Preliminaries
2 Differentiability, convexity and optimization in Banach spaces
3 Fixed-point theorems and their applications
4 Nonsmooth analysis: the subdifferential
5 Minimax theorems and duality
6 The calculus of variations
7 Variational inequalities
8 Critical point theory
9 Monotone-type operators
Bibliography
Index

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