Dumitru Motreanu Knihy

The book explores boundary value problems (BVPs) categorized into variational and hemivariational inequalities, emphasizing their distinct characteristics. The variational inequalities relate to convex energy functions, while hemivariational inequalities address nonconvex scenarios, a field that emerged in 1981. It highlights the rapid advancements in both theoretical and applied mathematics, particularly in engineering, due to the introduction of innovative mathematical methods. The text showcases significant progress in solving complex problems across various scientific disciplines.

The book delves into nonsmooth variational problems related to boundary value issues characterized by nonsmooth data and constraints. It covers a range of topics, including multivalued elliptic problems, variational inequalities, and hemivariational inequalities, along with their evolution problems. This specialized exploration highlights the complexities and mathematical intricacies involved in these types of variational challenges.

This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.