Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let  $u, v$ be  positive numbers. In this paper, we show  that  the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for fi...

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 a...

In this paper hemivariational inequality with nonhomogeneous Neumann boundary condition is investigated. The existence of infinitely many small solutions involving a class of p(x)−Laplacian equation in a smooth bounded domain is established. Our main tool is based on a version of the symmetric mountain pass lemma due to Kajikiya and the principle of symmetric criticality for a locally Lipschitz...

This paper deals with the existence and uniqueness of results for a class of hemivariational inequality problem. β1(x,y)+β2(x,y)+ J0(x;y− x) 0. Moreover, we enhance the main results an application to the existence of solution for a differential inclusion.

In the paper an elliptic quasi–variational–hemivariational inequality with constraints in a Banach space is studied. First, we apply Minty technique, KKM principle and theory of nonsmooth analysis to establish solvability problem. Then, employ generalized penalty regularization method for introduce family penalized regularized problems no Gâteaux differentiable potentials. Through limit procedu...

In this paper, we provide an alternative approach to establish the solution existence and uniqueness for elliptic variational-hemivariational inequalities. The new is based on elementary r...

The present paper is devoted to the study of the existence solution problem for a hemivariational inequality on vector-valued function space in the case when the nonlinear nonconvex part satisfies the unilateral growth condition. The critical point theory combined with the Galerkin approximation method have been used to establish the result.

we introduce variational inequality problems on hilbert $c^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. then relation between variational inequalities, $c^*$-valued metric projection and fixed point theory  on  hilbert $c^*$-modules is studied.