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 The presentation includes many recent results, including some that were previously unpublished.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.

Topological Degree Theory and Applications
Topological Degree Theory and Applications

Author: Yeol Je Cho

Publisher: CRC Press

Published: 2006-03-27

Total Pages: 228

ISBN-13: 1420011480

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Since the 1960s, many researchers have extended topological degree theory to various non-compact type nonlinear mappings, and it has become a valuable tool in nonlinear analysis. Presenting a survey of advances made in generalizations of degree theory during the past decade, this book focuses on topological degree theory in normed spaces and its ap

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.

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities
Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

Author: Dumitru Motreanu

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 320

ISBN-13: 146154064X

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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 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.

Multiple Solutions Of Boundary Value Problems: A Variational Approach
Multiple Solutions Of Boundary Value Problems: A Variational Approach

Author: John R Graef

Publisher: World Scientific

Published: 2015-08-26

Total Pages: 290

ISBN-13: 9814696560

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Variational methods and their generalizations have been verified to be useful tools in proving the existence of solutions to a variety of boundary value problems for ordinary, impulsive, and partial differential equations as well as for difference equations. In this monograph, we look at how variational methods can be used in all these settings. In our first chapter, we gather the basic notions and fundamental theorems that will be applied in the remainder of this monograph. While many of these items are easily available in the literature, we gather them here both for the convenience of the reader and for the purpose of making this volume somewhat self-contained. Subsequent chapters deal with the Sturm-Liouville problems, multi-point boundary value problems, problems with impulses, partial differential equations, and difference equations. An extensive bibliography is also included.

The Mountain Pass Theorem
The Mountain Pass Theorem

Author: Youssef Jabri

Publisher: Cambridge University Press

Published: 2003-09-15

Total Pages: 390

ISBN-13: 9781139440813

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This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a complete and unified way. Coverage includes standard topics, but it also covers other topics covered nowhere else in book form: the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. Each chapter has a section with supplementary comments and bibliographical notes, and there is a rich bibliography and a detailed index to aid the reader. The book is suitable for researchers and graduate students. Nevertheless, the style and the choice of the material make it accessible to all newcomers to the field.

Complementarity, Duality and Symmetry in Nonlinear Mechanics
Complementarity, Duality and Symmetry in Nonlinear Mechanics

Author: David Yang Gao

Publisher: Springer Science & Business Media

Published: 2012-11-08

Total Pages: 429

ISBN-13: 9048195772

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Complementarity, duality, and symmetry are closely related concepts, and have always been a rich source of inspiration in human understanding through the centuries, particularly in mathematics and science. The Proceedings of IUTAM Symposium on Complementarity, Duality, and Symmetry in Nonlinear Mechanics brings together some of world's leading researchers in both mathematics and mechanics to provide an interdisciplinary but engineering flavoured exploration of the field's foundation and state of the art developments. Topics addressed in this book deal with fundamental theory, methods, and applications of complementarity, duality and symmetry in multidisciplinary fields of nonlinear mechanics, including nonconvex and nonsmooth elasticity, dynamics, phase transitions, plastic limit and shakedown analysis of hardening materials and structures, bifurcation analysis, entropy optimization, free boundary value problems, minimax theory, fluid mechanics, periodic soliton resonance, constrained mechanical systems, finite element methods and computational mechanics. A special invited paper presented important research opportunities and challenges of the theoretical and applied mechanics as well as engineering materials in the exciting information age. Audience: This book is addressed to all scientists, physicists, engineers and mathematicians, as well as advanced students (doctoral and post-doctoral level) at universities and in industry.