We generalize the concept of well-posedness by perturbations for optimization problem to a class of variational-hemivariational inequalities. We establish some metric characterizations of the well-posedness by perturbations for the variational-hemivariational inequality and prove their equivalence between the well-posedness by perturbations for the variational-hemivariational inequality and the...

In this paper, the concept of well-posedness for a minimization problem is extended to develop the concept of well-posedness for a class of strongly mixed variationalhemivariational inequalities with perturbations which includes as a special case the class of variational-hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed strongly mixed...

A class of variational-hemivariational inequalities is studied in this paper. An inequality in the class involves two nonlinear operators and two nondifferentiable functionals, of which at least one is convex. An existence and uniqueness result is proved for a solution of the inequality. Continuous dependence of the solution on the data is shown. Convergence is established rigorously for finite...

‎This paper aims at establishing the existence and uniqueness of solutions for a nonstandard variational-hemivariational inequality. The solutions of this inequality are discussed in a subset $K$ of a reflexive Banach space $X$. Firstly, we prove the existence of solutions in the case of bounded closed and convex subsets. Secondly, we also prove the case when $K$ is compact convex subsets. Fina...

Variational–hemivariational inequalities are useful in applications in science and engineering. This paper is devoted to numerical analysis for an evolutionary variational–hemivariational inequality. We introduce a fully discrete scheme for the inequality, using a finite element approach for the spatial approximation and a backward finite difference to approximate the time derivative. We presen...

In this work, we used reflexive Banach spaces to study the differential variational—hemivariational inequality problems with constraints. We established a sequence of perturbed variational–hemivariational constraints and penalty coefficients. Then, for each inequality, proved unique solvability convergence solutions problems. Following that, proposed mathematical model viscoelastic rod in unila...

A system of a first order history-dependent evolutionary variational-hemivariational inequality with unilateral constraints coupled nonlinear ordinary differential equation in Banach space is studied. Based on fixed point theorem for history dependent operators, results the well-posedness are proved. Existence, uniqueness, continuous dependence solution data, and regularity established. Two app...

In the present paper, we generalize the concept of well-posedness to a generalized hemivariational inequality, give some metric characterizations of the α-well-posed generalized hemivariational inequality, and derive some conditions under which the generalized hemivariational inequality is strongly α-well-posed in the generalized sense. Also, we show that the α-well-posedness of the generalized...

In this paper we prove the principle of symmetric criticality for Motreanu–Panagiotopoulos type functionals, i.e., for convex, proper, lower semicontinuous functionals which are perturbed by a locally Lipschitz function. By means of this principle a variational–hemivariational inequality is studied on certain type of unbounded strips. © 2006 Elsevier Inc. All rights reserved.

The present paper is devoted to the stability analysis of a general class of hemivariational inequalities. Essentially, we present two approaches for this class of problems. First, using a general version of Minty’s Lemma and the convergence result of generalized gradients due to T. Zolezzi [23], we prove a stability result in the spirit of Mosco’s results on the variational inequalities [14]. ...