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Full Description
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.
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.
