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Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems (Hardcover, 2003 ed.): Dumitru... Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems (Hardcover, 2003 ed.)
Dumitru Motreanu, Vicentiu D. Radulescu
R3,260 Discovery Miles 32 600 Ships in 10 - 15 working days

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."

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities (Hardcover, 1999 ed.): Dumitru... Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities (Hardcover, 1999 ed.)
Dumitru Motreanu, Panagiotis D. Panagiotopoulos
R4,743 Discovery Miles 47 430 Ships in 12 - 19 working days

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."

Variational and Hemivariational Inequalities - Theory, Methods and Applications - Volume II: Unilateral Problems (Hardcover,... Variational and Hemivariational Inequalities - Theory, Methods and Applications - Volume II: Unilateral Problems (Hardcover, 2003 ed.)
D. Goeleven, Dumitru Motreanu
R3,245 Discovery Miles 32 450 Ships in 10 - 15 working days

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.

Nonsmooth Variational Problems and Their Inequalities - Comparison Principles and Applications (Hardcover, 2007 ed.): Siegfried... Nonsmooth Variational Problems and Their Inequalities - Comparison Principles and Applications (Hardcover, 2007 ed.)
Siegfried Carl, Vy K. Le, Dumitru Motreanu
R3,268 Discovery Miles 32 680 Ships in 10 - 15 working days

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.

Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems (Hardcover, 2014 ed.): Dumitru... Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems (Hardcover, 2014 ed.)
Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou
R3,885 Discovery Miles 38 850 Ships in 12 - 19 working days

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.

Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems (Paperback, Softcover reprint of the... Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems (Paperback, Softcover reprint of the original 1st ed. 2014)
Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou
R3,075 Discovery Miles 30 750 Ships in 10 - 15 working days

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.

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities (Paperback, Softcover reprint of... Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities (Paperback, Softcover reprint of the original 1st ed. 1999)
Dumitru Motreanu, Panagiotis D. Panagiotopoulos
R4,584 Discovery Miles 45 840 Ships in 10 - 15 working days

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."

Variational and Hemivariational Inequalities Theory, Methods and Applications - Volume I: Unilateral Analysis and Unilateral... Variational and Hemivariational Inequalities Theory, Methods and Applications - Volume I: Unilateral Analysis and Unilateral Mechanics (Paperback, Softcover reprint of the original 1st ed. 2003)
D. Goeleven, Dumitru Motreanu, Y. Dumont, M. Rochdi
R1,638 Discovery Miles 16 380 Ships in 10 - 15 working days

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 Non-variational Methods in Nonlinear Analysis and Boundary Value Problems (Paperback, Softcover reprint of the... Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems (Paperback, Softcover reprint of the original 1st ed. 2003)
Dumitru Motreanu, Vicentiu D. Radulescu
R3,127 Discovery Miles 31 270 Ships in 10 - 15 working days

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."

Nonsmooth Variational Problems and Their Inequalities - Comparison Principles and Applications (Paperback, Softcover reprint of... Nonsmooth Variational Problems and Their Inequalities - Comparison Principles and Applications (Paperback, Softcover reprint of hardcover 1st ed. 2007)
Siegfried Carl, Vy K. Le, Dumitru Motreanu
R3,055 Discovery Miles 30 550 Ships in 10 - 15 working days

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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