Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities / Edition 1

by Dumitru Motreanu, Panagiotis D. Panagiotopoulos

Overview

Boundary value problems which have variational expressions in form of inequal­ ities can be divided into two main classes. The class of boundary value problems (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.

Product Details

ISBN-13:	9780792354567
Publisher:	Springer US
Publication date:	12/31/1998
Series:	Nonconvex Optimization and Its Applications , #29
Edition description:	1999
Pages:	310
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

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.

Editorial Reviews

Motreanu (mathematics, University of Iasi, Romania) and Panagiotopoulos (civil engineering, Aristotle University, Greece) consider the qualitative properties of the solutions of hemivariational inequalities. To this end, they deal with the mathematical theory of eigenvalue problems for the same. This new type of eigenvalue problem arises, for example, in the variational formulation of mechanical problems whenever nonconvex nonsmooth energy functionals are involved. New existence, multiplicity and pertubation results are proved using three different approaches: minimization, minimax methods, and (sub)critical point theory. Nonresonant and resonant cases are studied both for static and dynamic problems. Applications concerning new stability results for beams, plates and shells with adhesive supports illustrate the theory. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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