Dumitru Motreanu's Books

Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems

By: Dumitru Motreanu,Vicentiu D. Radulescu

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Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems

By: Dumitru Motreanu,Vicentiu D. Radulescu

This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.

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400

Publisher

Springer Science & Business Media

Published Date

ISBN 10

140201385X

ISBN 13

9781402013850

Tangency, Flow Invariance for Differential Equations, and Optimization Problems

By: Nicolae H. Pavel,Dumitru Motreanu

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Tangency, Flow Invariance for Differential Equations, and Optimization Problems

By: Nicolae H. Pavel,Dumitru Motreanu

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.

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Page Count

504

Publisher

CRC Press

Published Date

ISBN 10

0824773411

ISBN 13

9780824773410

Variational and Hemivariational Inequalities - Theory, Methods and Applications

Volume II: Unilateral Problems

By: D. Goeleven,Dumitru Motreanu

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Variational and Hemivariational Inequalities - Theory, Methods and Applications

Volume II: Unilateral Problems

By: D. Goeleven,Dumitru Motreanu

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.

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Page Count

361

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441987584

ISBN 13

9781441987587

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

By: Dumitru Motreanu,Panagiotis D. Panagiotopoulos

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Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

By: Dumitru Motreanu,Panagiotis D. Panagiotopoulos

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.

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Page Count

320

Publisher

Springer Science & Business Media

Published Date

ISBN 10

146154064X

ISBN 13

9781461540649

Nonlinear Differential Problems with Smooth and Nonsmooth Constraints

By: Dumitru Motreanu

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Nonlinear Differential Problems with Smooth and Nonsmooth Constraints

By: Dumitru Motreanu

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. - Builds from functional analysis and operator theory, to nonlinear elliptic systems and control problems - Outlines the evolution of the main ideas of nonlinear analysis and their roots in classical mathematics - Presented with numerous end-of-chapter exercises and sophisticated open problems - Illustrated with pertinent industrial and engineering numerical examples and applications - Accompanied by hundreds of curated references, saving readers hours of research in conducting literature analysis

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364

Publisher

Academic Press

Published Date

ISBN 10

0128133937

ISBN 13

9780128133934

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

By: Dumitru Motreanu,Panagiotis D. Panagiotopoulos

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Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

By: Dumitru Motreanu,Panagiotis D. Panagiotopoulos

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320

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Springer Science & Business Media

Published Date

ISBN 10

146154064X

ISBN 13

9781461540649

Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

By: Dumitru Motreanu,Viorica Venera Motreanu,Nikolaos Papageorgiou

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Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

By: Dumitru Motreanu,Viorica Venera Motreanu,Nikolaos Papageorgiou

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.

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Page Count

465

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461493234

ISBN 13

9781461493235

Tangency, Flow Invariance for Differential Equations, and Optimization Problems

By: Nicolae H. Pavel,Dumitru Motreanu

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Tangency, Flow Invariance for Differential Equations, and Optimization Problems

By: Nicolae H. Pavel,Dumitru Motreanu

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504

Publisher

CRC Press

Published Date

ISBN 10

0824773411

ISBN 13

9780824773410

Variational and Hemivariational Inequalities Theory, Methods and Applications

Volume I: Unilateral Analysis and Unilateral Mechanics

By: D. Goeleven,Dumitru Motreanu,Y. Dumont,M. Rochdi

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Variational and Hemivariational Inequalities Theory, Methods and Applications

Volume I: Unilateral Analysis and Unilateral Mechanics

By: D. Goeleven,Dumitru Motreanu,Y. Dumont,M. Rochdi

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Page Count

417

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441986103

ISBN 13

9781441986108

Variational and Hemivariational Inequalities - Theory, Methods and Applications

Volume II: Unilateral Problems

By: DANIEL Goeleven,Dumitru Motreanu

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Variational and Hemivariational Inequalities - Theory, Methods and Applications

Volume II: Unilateral Problems

By: DANIEL Goeleven,Dumitru Motreanu

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Page Count

372

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402075383

ISBN 13

9781402075384

Nonsmooth Variational Problems and Their Inequalities

Comparison Principles and Applications

By: Siegfried Carl,Vy Khoi Le,Dumitru Motreanu

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Nonsmooth Variational Problems and Their Inequalities

Comparison Principles and Applications

By: Siegfried Carl,Vy Khoi Le,Dumitru Motreanu

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.

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404

Publisher

Springer Science & Business Media

Published Date

ISBN 10

038746252X

ISBN 13

9780387462523

Variational and Hemivariational Inequalities - Theory, Methods and Applications

Volume II: Unilateral Problems

By: DANIEL Goeleven,Dumitru Motreanu

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Variational and Hemivariational Inequalities - Theory, Methods and Applications

Volume II: Unilateral Problems

By: DANIEL Goeleven,Dumitru Motreanu

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Page Count

354

Publisher

Springer

Published Date

ISBN 10

1441987592

ISBN 13

9781441987594

Variational and Hemivariational Inequalities Theory, Methods and Applications

Volume I: Unilateral Analysis and Unilateral Mechanics

By: D. Goeleven,Dumitru Motreanu

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Variational and Hemivariational Inequalities Theory, Methods and Applications

Volume I: Unilateral Analysis and Unilateral Mechanics

By: D. Goeleven,Dumitru Motreanu

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Page Count

428

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1402075375

ISBN 13

9781402075377

Book's by Dumitru Motreanu

Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems

Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems

Tangency, Flow Invariance for Differential Equations, and Optimization Problems

Tangency, Flow Invariance for Differential Equations, and Optimization Problems

Variational and Hemivariational Inequalities - Theory, Methods and Applications

Variational and Hemivariational Inequalities - Theory, Methods and Applications

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

Nonlinear Differential Problems with Smooth and Nonsmooth Constraints

Nonlinear Differential Problems with Smooth and Nonsmooth Constraints

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

Tangency, Flow Invariance for Differential Equations, and Optimization Problems

Tangency, Flow Invariance for Differential Equations, and Optimization Problems

Variational and Hemivariational Inequalities Theory, Methods and Applications

Variational and Hemivariational Inequalities Theory, Methods and Applications

Variational and Hemivariational Inequalities - Theory, Methods and Applications

Variational and Hemivariational Inequalities - Theory, Methods and Applications

Nonsmooth Variational Problems and Their Inequalities

Nonsmooth Variational Problems and Their Inequalities

Variational and Hemivariational Inequalities - Theory, Methods and Applications

Variational and Hemivariational Inequalities - Theory, Methods and Applications

Variational and Hemivariational Inequalities Theory, Methods and Applications

Variational and Hemivariational Inequalities Theory, Methods and Applications

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