Nonlinear Differential Problems with Smooth and Nonsmooth Constraints systematically evaluates how to solve boundary value problems with smooth and nonsmooth constraints. Primarily covering nonlinear elliptic eigenvalue problems and quasilinear elliptic problems using techniques amalgamated from a range of sophisticated nonlinear analysis domains, the work is suitable for PhD and other early career researchers seeking solutions to nonlinear differential equations. Although an advanced work, the book is self-contained, requiring only graduate-level knowledge of functional analysis and topology. Whenever suitable, open problems are stated and partial solutions proposed. The work is accompanied by end-of-chapter problems and carefully curated references.

Nonlinear Differential Problems with Smooth and Nonsmooth Constraints (Mathematical Analysis and its Applications)

Science & Math

Motreanu, Dumitru

Mathematics

Academic Press

This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.

Nonsmooth Variational Problems and Their Inequalities: Comparison Principles and Applications (Springer Monographs in Mathematics)

Carl, Siegfried

Le, Vy Khoi

Springer

Boundary value problems which have variational expressions in form of inequal ities can be divided into two main classes. The class of boundary value prob lems (BVPs) leading to variational inequalities and the class of BVPs leading to hemivariational inequalities. The first class is related to convex energy functions and has being studied over the last forty years and the second class is related to nonconvex energy functions and has a shorter research "life" beginning with the works of the second author of the present book in the year 1981. Nevertheless a variety of important results have been produced within the framework of the theory of hemivariational inequalities and their numerical treatment, both in Mathematics and in Applied Sciences, especially in Engineering. It is worth noting that inequality problems, i. e. BVPs leading to variational or to hemivariational inequalities, have within a very short time had a remarkable and precipitate development in both Pure and Applied Mathematics, as well as in Mechanics and the Engineering Sciences, largely because of the possibility of applying and further developing new and efficient mathematical methods in this field, taken generally from convex and/or nonconvex Nonsmooth Analy sis. The evolution of these areas of Mathematics has facilitated the solution of many open questions in Applied Sciences generally, and also allowed the formu lation and the definitive mathematical and numerical study of new classes of interesting problems.

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities (Nonconvex Optimization and Its Applications, 29)

Panagiotopoulos, Panagiotis D.

"Provides a great deal of material that is completely new to the field of flow invariance, offering fresh insights for experienced mathematicians and rigorous training for students new to the specialty. Four useful appendices supply the methods used throughout the book, making it a totally self-referential and self-contained unit. Features many results that are exclusive to the authors."

Tangency, Flow Invariance for Differential Equations, and Optimization Problems (Chapman & Hall/CRC Pure and Applied Mathematics)

Pavel, Nicolae H.

CRC-Press

This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time.

Variational and Hemivariational Inequalities Theory, Methods and Applications: Volume I: Unilateral Analysis and Unilateral Mechanics (Nonconvex Optimization and Its Applications)

Goeleven, D.

Dumont, Y.

Rochdi, M.

This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time.  Audience: The book is suitable for researchers, and for doctoral and post-doctoral courses.

Variational and Hemivariational Inequalities - Theory, Methods and Applications (Volume 2 Unilateral Problems)

This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time.

Variational and Hemivariational Inequalities - Theory, Methods and Applications: Volume II: Unilateral Problems (Nonconvex Optimization and Its Applications) (Vol 2)

This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.

See the best price to sell, buy, or rent books by Motreanu, Dumitru. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Motreanu, Dumitru

See the best price to sell, buy, or rent books by Motreanu, Dumitru. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Nonlinear Differential Problems with Smooth and Nonsmooth Constraints (Mathematical Analysis and its Applications)

Nonsmooth Variational Problems and Their Inequalities: Comparison Principles and Applications (Springer Monographs in Mathematics)

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities (Nonconvex Optimization and Its Applications, 29)

Tangency, Flow Invariance for Differential Equations, and Optimization Problems (Chapman & Hall/CRC Pure and Applied Mathematics)

Variational and Hemivariational Inequalities Theory, Methods and Applications: Volume I: Unilateral Analysis and Unilateral Mechanics (Nonconvex Optimization and Its Applications)

Variational and Hemivariational Inequalities - Theory, Methods and Applications (Volume 2 Unilateral Problems)

Variational and Hemivariational Inequalities - Theory, Methods and Applications: Volume II: Unilateral Problems (Nonconvex Optimization and Its Applications) (Vol 2)

Nonsmooth Variational Problems and Their Inequalities: Comparison Principles and Applications (Springer Monographs in Mathematics)

Variational and Hemivariational Inequalities Theory, Methods and Applications: Volume I: Unilateral Analysis and Unilateral Mechanics (Nonconvex Optimization and Its Applications)

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities (Nonconvex Optimization and Its Applications, 29)