Formally we have arrived at the middle of the book. So you may need a pause for recovering, a pause which we want to fill up by some fixed point theorems supplementing those which you already met or which you will meet in later chapters. The first group of results centres around Banach’s fixed point theorem. The latter is certainly a nice result since it contains only one simple condition on the map F, since it is so easy to prove and since it nevertheless allows a variety of applications. Therefore it is not astonishing that many mathematicians have been attracted by the question to which extent the conditions on F and the space Ω can be changed so that one still gets the existence of a unique or of at least one fixed point. The number of results produced this way is still finite, but of a statistical magnitude, suggesting at a first glance that only a random sample can be covered by a chapter or even a book of the present size. Fortunately (or unfortunately?) most of the modifications have not found applications up to now, so that there is no reason to write a cookery book about conditions but to write at least a short outline of some ideas indicating that this field can be as interesting as other chapters. A systematic account of more recent ideas and examples in fixed point theory should however be written by one of the true experts. Strange as it is, such a book does not seem to exist though so many people are puzzling out so many results.

Fixed Point Theory

Convex Analysis: (pms-28)

This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.

Variational Methods for Nonlocal Fractional Problems

nonlinear functional analysis and its applications is available in our book collection an online access to it is set as public so you can get it instantly. Our books collection hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the nonlinear functional analysis and its applications is universally compatible with any devices to read.

Nonlinear Functional Analysis And Its Applications

This text provides a complete introduction to the theory of variational inequalities with emphasis on contact mechanics. It covers existence, uniqueness and convergence results for variational inequalities, including the modelling and variational analysis of specific frictional contact problems with elastic, viscoelastic and viscoplastic materials. New models of contact are presented, including contact of piezoelectric materials. Particular attention is paid to the study of history-dependent quasivariational inequalities and to their applications in the study of contact problems with unilateral constraints. The book fully illustrates the cross-fertilisation between modelling and applications on the one hand and nonlinear mathematical analysis on the other. Indeed, the reader will gain an understanding of how new and nonstandard models in contact mechanics lead to new types of variational inequalities and, conversely, how abstract results concerning variational inequalities can be applied to prove the unique solvability of the corresponding contact problems.

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Mathematical Models in Contact Mechanics

Preface. 1. Elements of Nonsmooth Analysis. Hemivariational Inequalities. 2. Nonsmooth Critical Point Theory. 3. Minimax Methods for Variational-Hemivariational Inequalities. 4. Eigenvalue Problems for Hemivariational Inequalities. 5. Multiple Solutions of Eigenvalue Problems for Hemivariational Inequalities. 6. Eigenvalue Problems for Hemivariational Inequalities on the Sphere. 7. Resonant Eigenvalue Problems for Hemivariational Inequalities. 8. Double Eigenvalue Problems for Hemivariational Inequalities. 9. Periodic and Dynamic Problems.

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Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

Nonsmooth Variational Problems and Their Inequalities

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Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

Mathematical Preliminaries- Variational Equations- Multivalued Variational Equations- Variational Inequalities- Hemivariational Inequalities- Variational-Hemivariational Inequalities

Nonsmooth Variational Problems And Their Inequalities: Comparison Principles And Applications

Preface. Introduction. 1. Elements of Nonsmooth Analysis. 1. Generalized Gradients of Locally Lipschitz Functionals. 2. Palais Smale Condition and Coerciveness for a Class of Nonsmooth Functionals. 3. Nonsmooth Analysis in the Sense of Degiovanni. 2. Variational Methods. 1. Critical Point Theory for Locally Lipschitz Functionals. 2. Critical Point Theory for Convex Perturbations of Locally Lipschitz Functionals. 3. A Critical Point Theory in Metric Spaces. 3. Variational Methods. 1. Critical Point Theory for Convex Perturbations of Locally Lipschitz Functionals in the Limit Case. 2. Examples. 4. Multivalued Elliptic Problems in Variational Form. 1. Multiplicity for Locally Lipschitz Periodic Functionals. 2. The Multivalued Forced-pendulum Problem. 3. Hemivariational Inequalities Associated to Multivalued Problems with Strong Resonance. 4. A Parallel Nonsmooth Critical Point Theory. Approach to Stationary Schrodinger Type Equations in Constraints. 8. Non-Symmetric Perturbations of Symmetric Eigenvalue Problems. 1. Non-Symmetric Perturbations of Eigenvalue Problems for Periodic Hemivariational Inequalities with Constraints. 2. Perturbations of Double of Eigenvalue Problems for General Hemivariational Inequalities with Constraints. 3. location of Solutions by Minimax Methods of Variational Hemivariational Inequalities. 10. Nonsmooth Evolution Problems. 1. First Order Evolution Variational Inequalities. 2. Second Order Evolution Variational Inequalities. 3. Stability Problems for Evolution Variational Inequalities. 11. Inequality Problems in BV and Geometric Applications. 1. The General Framework. 2. Area Type Functionals. 3. A Result of Clark Type. 4. An Inequality Problem with Superlinear Potential.

Dumitru Motreanu

Papers

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

Nonsmooth Variational Problems and Their Inequalities

Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

Nonsmooth Variational Problems And Their Inequalities: Comparison Principles And Applications

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