Variational and Monotonicity Methods in Nonsmooth Analysis

This book provides a modern and comprehensive presentation of a wide variety of problems arising in nonlinear analysis, game theory, engineering, mathematical physics and contact mechanics. It includes recent achievements and puts them into the context of the existing literature.

The volume is organized in four parts. Part I contains fundamental mathematical results concerning convex and locally Lipschits functions. Together with the Appendices, this foundational part establishes the self-contained character of the text. As the title suggests, in the following sections, both variational and topological methods are developed based on critical and fixed point results for nonsmooth functions. The authors employ these methods to handle the exemplary problems from game theory and engineering that are investigated in Part II, respectively Part III. Part IV is devoted to applications in contact mechanics.

The book will be of interest to PhD students and researchers in applied mathematics as well as specialists working in nonsmooth analysis and engineering.

Alexandru Kristaly is a professor of mathematics at the Department of Economics of the Babes-Bolyai University (Cluj-Napoca, Romania) and a research professor at the Obuda University (Budapest, Hungary). He is doing research in calculus of variations and geometric analysis, mainly focusing to elliptic PDEs, Riemann-Finsler geometry andequilibrium problems. He obtained twice the Janos Bolyai Research Fellowship of the Hungarian Academy of Sciences, and visited various research institutes as City University of Hong Kong, Institut des Hautes Études Scientifiques, Istituto Nazionale di Alta Matematica, Universitat Bern, etc. He is the leader of several research grants.

 Csaba Gyorgy Varga is a professor of mathematics at the Department of Mathematics of the Babes-Bolyai University (Cluj-Napoca, Romania). His main research areas are topological and variational methods in the study of smooth and nonsmooth elliptic problems, including variational inequalities and differential inclusions. He has over 100 research papers with a broad variety of co-authors in various journals. He was a visiting professor at University of Perugia, University of Catania, Eotvos Lorand University, and others, being invited as a main speaker to various conferences. He supervised a number of PhD Students and has been the leader of research grants.