Convergence of a generalized penalty method for variational–hemivariational inequalities

The aim the paper is to study a large class of variational-hemivariational inequalities involving constraints in Banach space. First, we establish general existence theorem for this class. Second, introduce sequence penalized problems without constraints. Under suitable assumptions, prove that Kuratowski upper limit with respect weak topology sets solutions problems, w--lim supn??Sn, nonempty and contained set original inequality problem. Also, identity, supn??Sn=s--lim when operator A satisfies (S)+-property. Finally, illustrate applicability theoretical results explore two complicated partial differential systems elliptic type, which are an mixed boundary value problem nonlinear nonhomogeneous obstacle effect, elastic contact mechanics unilateral constraints, respectively.