In this paper, we give some existence results for equilibrium problems
by proceeding to a perturbation of the initial problem and using techniques of recession analysis. We develop and describe thoroughly recession condition which
ensure existence of at least one solution for hemivariational inequalities introduced
by Panagiotopoulos. Then we give two applications to resolution of concrete variational inequalities. We shall examine two examples. The first one concerns the
unilateral boundary condition. In the second, we shall consider the contact problem
with given friction on part of the boundary.