Variational and Monotonicity Methods in Nonsmooth Analysis: (Frontiers in Mathematics)

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.

Table of Contents:
- Part I Mathematical Background. - 1. Convex and Lower Semicontinuous Functionals. - 2. Locally Lipschitz Functionals. - 3. Critical Points, Compactness Conditions and Symmetric Criticality. - Part II Variational Techniques in Nonsmooth Analysis and Applications. - 4. Deformation Results. - 5. Minimax and Multiplicity Results. - 6. Existence and Multiplicity Results for Differential Inclusions on Bounded Domains. - 7. Hemivariational Inequalities and Differential Inclusions on Unbounded Domains. - Part III Topological Methods for Variational and Hemivariational Inequalities. - 8. Fixed Point Approach. - 9. Nonsmooth Nash Equilibria on Smooth Manifolds. - 10. Inequality Problems Governed by Set-valued Maps of Monotone Type. - Part IV Applications to Nonsmooth Mechanics. - 11. Antiplane Shear Deformation of Elastic Cylinders in Contact with a Rigid Foundation. - 12. Weak Solvability of Frictional Problems for Piezoelectric Bodies in Contact with a Conductive Foundation. - 13. The Bipotential Method for Contact Models with Nonmonotone Boundary Conditions.

About the Author :
Nicusor Costea is currently lecturer at the Department of Mathematics and Computer Science of the Politehnica University of Bucharest (Romania). He obtained a Ph.D. from University of Craiova in 2010 and a second Ph.D. from Central European University in 2015. He authored 22 papers covering various topics from nonsmooth analysis and contact mechanics such as existence results for variational and hemivariational inequalities, existence and multiplicity results for differential inclusions involving generalizations of the Laplace operator and mathematical modelling of various phenomena arising in the mechanics of deformable solids. 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.

Review :
“The book is a reliable reference for the main issues on these topics and gives a clear collection of recent results and applications in this important field of research. Moreover, the authors achieve a perfect balance between the possible needs of a Ph.D. student and those of an experienced researcher.” (Pasquale Candito, Mathematical Reviews, November, 2022) “The text is clearly written and systematic. The proofs are complete and the applications are consistent. The book is useful for researchers, and parts of it can be recommended as additional reading for postgraduate students.” (Petru Jebelean, zbMATH 1490.49001, 2022)