Basic Monotonicity Methods with Some Applications

by Marek Galewski

Overview

This textbook introduces some basic tools from the theory of monotone operators together with some of their applications. Examples that work for ordinary differential equations are provided. The illustrating material is kept relatively simple, while at the same time offering inspiring applications to the reader.

The material will appeal to graduate students in mathematics who want to learn some basics in the theory of monotone operators. Furthermore, it offers a smooth transition to studying more advanced topics pertaining to more refined applications by shifting to pseudomonotone operators, and next, to multivalued monotone operators.

Product Details

ISBN-13:	9783030753078
Publisher:	Springer International Publishing
Publication date:	09/02/2021
Series:	Compact Textbooks in Mathematics
Edition description:	1st ed. 2021
Pages:	180
Product dimensions:	6.10(w) x 9.25(h) x 0.00(d)

About the Author

Marek Galewski is a professor at the Institute of Mathematics of the Lodz University of Technology in Lodz, Poland.

Table of Contents

Preface.- Introduction to the topic of the course.- Some excerpts from functional analysis.- Monotone operators.- On the Fenchel-Young conjugate.- Potential operators.- Existence of solutions to abstract equations.- Normalized duality mapping.- On the Galerkin method.- Some selected applications.

Editorial Reviews

This monograph is an excellent addition to the literature on nonlinear analysis, especially the theory of monotone operators. … The presentation is brief, in large parts, but quite informative. This is a very readable text and is mostly self-contained. This should serve as a text for anyone who wants to know about the most important aspects of monotone operators, especially a researcher who wants to pursue the area of monotone operator theory.” (K. C. Sivakumar, zbMATH 1486.47001, 2022)

“I enjoyed reading this book and can confidently recommend it to any instructor teaching a course on monotonicity methods.” (Casey Timothy Cremins, Mathematical Reviews, June, 2022)

From the Publisher