Eigenvalue problems for variational-hemivariational inequalities in the sense of P. D. Panagiotopoulos

The aim of the paper is to present in an unifying way recent advances in th e study of variational-hemivariational inequalities in connection with new methods of nonsmooth critical point theory and optimization. A special atte ntion is paid to eigenvalue problems for variational-hemivariational inequa lities, where bifurcation phenomena are pointed out. Qualitative aspects as multiplicity and location of solutions are discussed. The obtained results allow to treat variational-hemivariational inequalities containing nonline arities with general growth conditions. The minimax methods described here can be applied not only for variational-hemivariational inequalities but al so for studying other problems in variational calculus, partial differentia l equations and unilateral analysis.