Basic Monotonicity Methods with Some Applications

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

• 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.

“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)