We consider a nonlinear Neumann problem driven by the p-Laplacian differential operator with a nonsmooth potential (hemivariational inequality). Using variational techniques based on the smooth critical point theory and the second deformation theorem, we prove an existence theorem and a multiplicity theorem, under hypothesis that in general do not imply the coercivity of the Euler functional.

A class of nonlinear Neumann problems driven by p(x)-Laplacian with a nonsmooth locally Lipschitz potential (hemivariational inequality) was considered. The approach used in this paper is the variational method for locally Lipschitz functions. More precisely, Weierstrass theorem and Mountain Pass theorem are used to prove the existence of at least two nontrivial solutions.

This problem can be considered as a nonconvex generalization of the classical variational inequalities of J. L. Lions and G. Stampacchia. For typical examples in connection with mechanics and engineering we refer to the books of Panagiotopoulos [20, 22] and [18]. The techniques used for resolution of hemivariational inequalities are subsequently based on arranging fixed point theorems, Galerkin...

We consider a nonlinear elliptic equation driven by the p-Laplacian with a nonsmooth potential hemivariational inequality and Dirichlet boundary condition. Using a variational approach based on nonsmooth critical point theory together with the method of upper and lower solutions, we prove the existence of at least three nontrivial smooth solutions: one positive, the second negative, and the thi...

This paper is concerned with existence results for inequality problems of type F0(u;v) + Ψ′(u;v) ≥ 0, for all v ∈ X , where X is a Banach space, F : X → R is locally Lipschitz, and Ψ : X → (−∞+∞] is proper, convex, and lower semicontinuous. Here F0 stands for the generalized directional derivative of F and Ψ′ denotes the directional derivative of Ψ. The applications we consider focus on the var...

In this paper we study the optimal control of system driven by hemivariational inequality of second order. First, we establish the existence of solutions to hemivariational inequality which contains nonlinear pseudomonotone evolution operator. Introducing a control variable in the multivalued term of the generalized subdifferential, we prove the closedness (in suitable topologies) of the graph ...

In this paper we trait hemivariational inequality systems. In certain case, this problem can be reduced to study a hemivariational inequality. Several applications are given as Browder and Hartmann-Stampacchia type results and Nash equilibrium point theorems. MSC 2000. 35J60, 49J35.

In this paper, we are devoted to exploring conditions of well-posedness for generalized hemivariational inequalities with Clarke’s generalized directional derivative in reflexive Banach spaces. By using some equivalent formulations of the generalized hemivariational inequality with Clarke’s generalized directional derivative under different monotonicity assumptions, we establish two kinds of co...

In this paper we consider hemivariational inequalities of hyperbolic type. The existence result for hemivariational inequality is given and the existence theorem for the optimal shape design problem is shown.

In this paper, minimax principles are explored for elliptic mixed hemivariational–variational inequalities. Under certain conditions, a saddle-point formulation is shown to be equivalent inequality. While the principle of independent interest, it employed in paper provide an elementary proof solution existence Theoretical results illustrated applications two contact problems.