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

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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The book provides a comprehensive exposition of modern topics in nonlinear analysis with applications to various boundary value problems with discontinuous nonlinearities and nonsmooth constraints. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. In addition to the existence of solutions, a major part of the book is devoted to the study of different qualitative properties such as multiplicity, location, extremality, and stability. The treatment relies on variational methods, monotonicity principles, topological arguments and optimization techniques. The book is based on the authors' original results obtained in the last decade. A great deal of the material is published for the first time in this book and is organized in a unifying way. The book is self-contained. The abstract results are illustrated through various examples and applications.

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The book provides a comprehensive exposition of modern topics in nonlinear analysis with applications to various boundary value problems with discontinuous nonlinearities and nonsmooth constraints. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. In addition to the existence of solutions, a major part of the book is devoted to the study of different qualitative properties such as multiplicity, location, extremality, and stability. The treatment relies on variational methods, monotonicity principles, topological arguments and optimization techniques. The book is based on the authors' original results obtained in the last decade. A great deal of the material is published for the first time in this book and is organized in a unifying way. The book is self-contained. The abstract results are illustrated through various examples and applications.
Content:
Front Matter....Pages i-xii
Elements of Nonsmooth Analysis....Pages 1-29
Critical Points for Nonsmooth Functionals....Pages 31-65
Variational Methods....Pages 67-98
Multivalued Elliptic Problems in Variational Form....Pages 99-137
Boundary Value Problems in Non-Variational Form....Pages 139-168
Variational, Hemivariational and Variational-Hemivariational Inequalities: Existence Results....Pages 169-210
Eigenvalue Problems with Symmetries....Pages 211-243
Non-Symmetric Perturbation of Symmetric Eigenvalue Problems....Pages 245-272
Location of Solutions for General Nonsmooth Problems....Pages 273-305
Nonsmooth Evolution Problems....Pages 307-347
Inequality Problems in BV and Geometric Applications....Pages 349-375
Back Matter....Pages 377-380

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The book provides a comprehensive exposition of modern topics in nonlinear analysis with applications to various boundary value problems with discontinuous nonlinearities and nonsmooth constraints. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. In addition to the existence of solutions, a major part of the book is devoted to the study of different qualitative properties such as multiplicity, location, extremality, and stability. The treatment relies on variational methods, monotonicity principles, topological arguments and optimization techniques. The book is based on the authors' original results obtained in the last decade. A great deal of the material is published for the first time in this book and is organized in a unifying way. The book is self-contained. The abstract results are illustrated through various examples and applications.
Content:
Front Matter....Pages i-xii
Elements of Nonsmooth Analysis....Pages 1-29
Critical Points for Nonsmooth Functionals....Pages 31-65
Variational Methods....Pages 67-98
Multivalued Elliptic Problems in Variational Form....Pages 99-137
Boundary Value Problems in Non-Variational Form....Pages 139-168
Variational, Hemivariational and Variational-Hemivariational Inequalities: Existence Results....Pages 169-210
Eigenvalue Problems with Symmetries....Pages 211-243
Non-Symmetric Perturbation of Symmetric Eigenvalue Problems....Pages 245-272
Location of Solutions for General Nonsmooth Problems....Pages 273-305
Nonsmooth Evolution Problems....Pages 307-347
Inequality Problems in BV and Geometric Applications....Pages 349-375
Back Matter....Pages 377-380
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