In this paper we examine a nonlinear hemivariational inequality of second order. The differential operator is set-valued, nonlinear and depends on both x and its gradient Dx. The same is true for the zero order term f , while the right-hand side nonlinearity satisfies a one-sided Lipschitz condition. We use the method of upper and lower solutions, coupled with truncation and penalization techni...

In this paper we consider a second order evolution inclusion with a coercive viscosity operator and a multivalued term of subdifferential form. The study is motivated by the dynamic problem of frictional contact between a viscoelastic piezoelectric deformable body and a foundation. The interaction between the body and the foundation is described, due to the skin effects, by a nonmonotone possib...

This paper studies an adhesive contact model which also takes into account the damage and long memory term. The deformable body is composed of a viscoelastic material process taken as quasistatic. caused by compression or tension involved in constitutive law function modelled through nonlinear parabolic inclusion. Meanwhile, adhesion bonding field on surface while d...

Abstract: A hemivariational inequality involving p-Laplacian is studied under the hypothesis that the nonlinear part fulfills the unilateral growth condition. The existence of solutions for problems with Neumann boundary conditions is established by making use of Chang’s version of the critical point theory for nonsmooth locally Lipschitz functionals, combined with the Galerkin method. The appr...

We consider a nonlinear Dirichlet parametric problem with discontinuous right hand side in which we have a competing effect of sub and superlinear nonlinearities. A bifurcation type result is studied when the parameter tends to zero.

Abstract. We consider a semilinear elliptic equation with a nonsmooth, locally 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...

Throughout the paper we use standard notations except special symbols introduced when they are defined. All spaces considered are Banach spaces whose norms are always denoted by ‖ · ‖. For any space V we consider its dual space V ? equipped with the strong topology. We denote by 〈·, ·〉 the duality pairing between V and V . Let f : V → R ∪ {∞} be an extended-real-valued function. Identifying ext...