Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

Softcover Nachdruck of the original 1. Auflage 1999
ISBN: 978-1-4613-6820-5
Verlag: Springer US

Buch, Englisch, Band 29, 310 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 505 g

Reihe: Nonconvex Optimization and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Panagiotopoulos, Panagiotis D.

Motreanu, Dumitru

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Mechanik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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.