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.

“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)

• 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.