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

Author: Dumitru Motreanu

Publisher: Springer Science & Business Media

Published: 2003-05-31

Total Pages: 400

ISBN-13: 9781402013850

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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.

Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems
Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

Author: Dumitru Motreanu

Publisher: Springer Science & Business Media

Published: 2013-11-19

Total Pages: 465

ISBN-13: 1461493234

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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.

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

Author: Dumitru Motreanu

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 384

ISBN-13: 1475769210

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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 Critical Point Theory and Nonlinear Boundary Value Problems
Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems

Author: Leszek Gasinski

Publisher: CRC Press

Published: 2004-07-27

Total Pages: 790

ISBN-13: 1420035037

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Starting in the early 1980s, people using the tools of nonsmooth analysis developed some remarkable nonsmooth extensions of the existing critical point theory. Until now, however, no one had gathered these tools and results together into a unified, systematic survey of these advances. This book fills that gap. It provides a complete presentation of nonsmooth critical point theory, then goes beyond it to study nonlinear second order boundary value problems. The authors do not limit their treatment to problems in variational form. They also examine in detail equations driven by the p-Laplacian, its generalizations, and their spectral properties, studying a wide variety of problems and illustrating the powerful tools of modern nonlinear analysis. The presentation includes many recent results, including some that were previously unpublished. Detailed appendices outline the fundamental mathematical tools used in the book, and a rich bibliography forms a guide to the relevant literature. Most books addressing critical point theory deal only with smooth problems, linear or semilinear problems, or consider only variational methods or the tools of nonlinear operators. Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods for a wide variety of problems.

Nonsmooth Variational Problems and Their Inequalities
Nonsmooth Variational Problems and Their Inequalities

Author: Siegfried Carl

Publisher: Springer Science & Business Media

Published: 2007-06-07

Total Pages: 404

ISBN-13: 038746252X

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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.

Noncoercive Variational Problems and Related Results
Noncoercive Variational Problems and Related Results

Author: Daniel Goeleven

Publisher: CRC Press

Published: 1996-10-10

Total Pages: 186

ISBN-13: 9780582304024

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In establishing a general theory of the existence of solutions for noncoercive variational problems and constrained problems formulated as variational inequalities or hemivariational inequalities, this Research Note illustrates recent mathematical approaches and results with various examples from mathematics and mechanics. The book unifies ideas for the treatment of various noncoercive problems and provides previously unpublished results for variational inequalities and hemivariational inequalities. The author points out important applications in mechanics and their mathfematical tratment using recession tools. This book will be of particular interest to researchers in pure and aplied mathematics and mechanics.

Variational Methods For Strongly Indefinite Problems
Variational Methods For Strongly Indefinite Problems

Author: Yanheng Ding

Publisher: World Scientific

Published: 2007-07-30

Total Pages: 177

ISBN-13: 9814474509

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This unique book focuses on critical point theory for strongly indefinite functionals in order to deal with nonlinear variational problems in areas such as physics, mechanics and economics. With the original ingredients of Lipschitz partitions of unity of gage spaces (nonmetrizable spaces), Lipschitz normality, and sufficient conditions for the normality, as well as existence-uniqueness of flow of ODE on gage spaces, the book presents for the first time a deformation theory in locally convex topological vector spaces. It also offers satisfying variational settings for homoclinic-type solutions to Hamiltonian systems, Schrödinger equations, Dirac equations and diffusion systems, and describes recent developments in studying these problems. The concepts and methods used open up new topics worthy of in-depth exploration, and link the subject with other branches of mathematics, such as topology and geometry, providing a perspective for further studies in these areas. The analytical framework can be used to handle more infinite-dimensional Hamiltonian systems.

Variational Methods in Shape Optimization Problems
Variational Methods in Shape Optimization Problems

Author: Dorin Bucur

Publisher: Springer Science & Business Media

Published: 2006-09-13

Total Pages: 218

ISBN-13: 0817644032

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Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.

Topological and Variational Methods for Nonlinear Boundary Value Problems
Topological and Variational Methods for Nonlinear Boundary Value Problems

Author: Pavel Drabek

Publisher: CRC Press

Published: 1997-04-17

Total Pages: 172

ISBN-13: 9780582309210

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In the rapidly developing area of nonlinear theory of differential equations, many important results have been obtained by the use of nonlinear functional analysis based on topological and variational methods. The survey papers presented in this volume represent the current state of the art in the subject. The methods outlined in this book can be used to obtain new results concerning the existence, uniqueness, multiplicity, and bifurcation of the solutions of nonlinear boundary value problems for ordinary and partial differential equations. The contributions to this volume are from well known mathematicians, and every paper contained in this book can serve both as a source of reference for researchers working in differential equations and as a starting point for those wishing to pursue research in this direction. With research reports in the field typically scattered in many papers within various journals, this book provides the reader with recent results in an accessible form.

The Method of Weighted Residuals and Variational Principles
The Method of Weighted Residuals and Variational Principles

Author: Bruce A. Finlayson

Publisher: SIAM

Published: 2013-12-30

Total Pages: 429

ISBN-13: 1611973236

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This classic book covers the solution of differential equations in science and engineering in such as way as to provide an introduction for novices before progressing toward increasingly more difficult problems. The Method of Weighted Residuals and Variational Principles describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles. The book also illustrates how to use simple methods to find approximate solutions, shows how to use the finite element method for more complex problems, and provides detailed information on error bounds. Problem sets make this book ideal for self-study or as a course text.