We conduct a detailed study of the existence theory for nonlinear hemivariational inequalities of second order. The problems under consideration are strongly nonlinear and not necessarily of variational nature. So we employ a variety of tools in order to solve them. More precisely, we use the general theory of nonlinear operators of monotone type, the method of upper-lower solutions, the multivalued Leray-Schauder principle, nonsmooth critical point theory coupled with Landesman-Lazer conditions and linking techniques and also truncation and penalization techniques. The problems that we examine involve Dirichlet boundary conditions; in the last section we also examine a problem with a nonhomogeneous and nonlinear Neumann boundary condition.
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm419-0-1,
author = {Nikolaos S. Papageorgiou and George Smyrlis},
title = {On nonlinear hemivariational inequalities},
series = {GDML\_Books},
year = {2003},
zbl = {1125.35034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm419-0-1}
}
Nikolaos S. Papageorgiou; George Smyrlis. On nonlinear hemivariational inequalities. GDML_Books (2003), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm419-0-1/