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báo cáo hóa học:" Research Article Infinitely Many Solutions for Perturbed Hemivariational Inequalities"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Infinitely Many Solutions for Perturbed Hemivariational Inequalities | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 363518 19 pages doi 10.1155 2010 363518 Research Article Infinitely Many Solutions for Perturbed Hemivariational Inequalities Giuseppina D Agui1 2 and Giovanni Molica Bisci3 1 DIMET Faculty of Engineering University of Reggio Calabria 89125 Reggio Calabria Italy 2 DiSIA Faculty of Engineering University of Messina 98122 Messina Italy 3 Department P.A.U. Architecture Faculty University of Reggio Calabria 89100 Reggio Calabria Italy Correspondence should be addressed to Giovanni Molica Bisci gmolica@unirc.it Received 8 September 2010 Accepted 28 November 2010 Academic Editor Raul F. Manasevich Copyright 2010 G. D Agul and G. Molica Bisci. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We deal with a perturbed eigenvalue Dirichlet-type problem for an elliptic hemivariational inequality involving the p-Laplacian. We show that an appropriate oscillating behaviour of the nonlinear part even under small perturbations ensures the existence of infinitely many solutions. The main tool in order to obtain our abstract results is a recent critical-point theorem for nonsmooth functionals. 1. Introduction Hemivariational inequalities appear in the mathematical modeling of several complicated mechanical and engineering problems whose relevant energy functionals are neither convex nor smooth. For instance this is the case of non-monotone multivalued interface laws or constitutive relations that occur in certain contact and friction processes as well as of phenomena related to large displacements and deformations expressed by nonlinear straindisplacement laws. The theory of hemivariational inequalities can be viewed as a new field of nonsmooth mechanics since the main ingredient used in the study of these inequalities is the notion of the Clarke