We consider a semilinear elliptic equation with a nonsmooth, locally
\hbox{Lipschitz} potential function (hemivariational inequality). Our
hypotheses permit double resonance at infinity and at zero (double-double
resonance situation). Our approach is based on the nonsmooth critical point
theory for locally Lipschitz functionals and uses an abstract multiplicity
result under local linking and an extension of the Castro--Lazer--Thews
reduction method to a nonsmooth setting, which we develop here using tools from
nonsmooth analysis.Comment: 23 page