An approach to semicoercive variational-hemivariational or hemivariational inequalities based on a recession technique introduced in (
), is developed. First, problems defined on vector-valued function spaces are considered under unilateral growth conditions imposed on nonlinear parts by making use of the Galerkin method. Second, a minimax method relying on Chang’s version of Mountain Pass Theorem for locally Lipschitz functionals (
) is applied to study semicoercive hemivariational inequalities on vector valued function spaces. Third, the resonant problem governed by the
-Laplacian involving the unilateral growth condition is discussed. Some mechanical problems as exemplifications of the presented approach are shown.