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Nonlinear Differential Problems with Smooth and Nonsmooth Constraints (Paperback): Dumitru Motreanu Nonlinear Differential Problems with Smooth and Nonsmooth Constraints (Paperback)
Dumitru Motreanu
R4,005 R3,624 Discovery Miles 36 240 Save R381 (10%) Ships in 12 - 17 working days

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.

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
R3,013 Discovery Miles 30 130 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
R4,497 Discovery Miles 44 970 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
R1,599 Discovery Miles 15 990 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
R3,067 Discovery Miles 30 670 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
R2,993 Discovery Miles 29 930 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.

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
R3,188 Discovery Miles 31 880 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.

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
R3,203 Discovery Miles 32 030 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
R4,690 Discovery Miles 46 900 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."

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
R4,617 Discovery Miles 46 170 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.

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
R3,211 Discovery Miles 32 110 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.

Handbook of Nonconvex Analysis and Applications (Paperback): David Yang Guo, Dumitru Motreanu Handbook of Nonconvex Analysis and Applications (Paperback)
David Yang Guo, Dumitru Motreanu
R1,816 Discovery Miles 18 160 Ships in 12 - 17 working days

Nonconvex analysis is a rapidly developing, multi-disciplinary field of research, comprehending theoretical analysis in mathematical modelling of natural systems, bifurcation and chaos in dynamical systems, finite deformation theory, nonlinear partial differential equations, global optimization, calculus of variation, numerical methods, and scientific computations. The field of nonconvex analysis has undergone considerable development in a remarkably short time-with extensive applications to theoretical physics, material science, modern mechanics, complex systems, and scientific computations. The present volume, Handbook of Nonconvex Analysis and Applications, consists of thirteen chapters written by notable experts in the field, addressing essential recent developments in nonconvex analysis and its applications, and keeping a balance between major areas of theory, methods, and applications. Each chapter provides an illuminating exposition of state-of-the-art approaches to a specific topic, with discussions of the central contributions, and pointers to some basic references. A variety of topics regarding nonconvex analysis and its applications are discussed: nonconvex variational principles; comparison principles; nonlinear eigenvalue problems; critical point theory; boundary value problems; topological methods, including Morse theory; nonlinear elliptic equations; evolution problems; difference equations; inequality problems; geometric properties of functions and spaces; and applications in mechanics. This Handbook will serve as a much-needed reference work for the dynamic and ever-growing field of nonconvex analysis and its applications.

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