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Minimax theorems and qualitative properties of the solutions of hemivariational inequalities. (English) Zbl 1060.49500

Nonconvex Optimization and Its Applications 29. Dordrecht: Kluwer Academic Publishers (ISBN 0-7923-5456-7/hbk). xviii, 309 p. (1999).
Publisher’s description: The present book is the first ever published in which a new type of eigenvalue problem is studied, one that is very useful for applications: eigenvalue problems related to hemivariational inequalities, i.e., involving nonsmooth, nonconvex energy functions. New existence, multiplicity and perturbation 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 and several new qualitative properties of the hemivariational inequalities are obtained. Both simple and double eigenvalue problems are studied, as well as those constrained on the sphere and those which are unconstrained. The book is self-contained, is written with the utmost possible clarity and contains highly original results. Applications concerning new stability results for beams, plates and shells with adhesive supports, etc. illustrate the theory. Audience: applied and pure mathematicians, civil, aeronautical and mechanical engineers.

MSC:

49J35 Existence of solutions for minimax problems
49J40 Variational inequalities
49-02 Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
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