Variational-hemivariational inequalities with nonhomogeneous Neumann boundary condition

  • Dumitru Motreanu
  • Patrick Winkert
Keywords: Elliptic variational-hemivariational inequality, Nonsmooth critical point theory, p-Laplacian.


The aim of this paper is the study of variational-hemivariational inequalities with nonhomogeneous Neumann boundary condition. Sufficient conditions for the existence of a whole sequence of solutions which is either unbounded or converges to zero are proved. For homogeneous Neumann boundary condition, results of this type have been obtained in Marano and Motreanu [3]. Our approach is based on abstract nonsmooth critical point results given in [3]. The applicability of our results is demonstrated by providing two verifiable criteria which address problems with nonsmooth potential and nonzero Neumann boundary condition.