A new class of quasistatic frictional contact problems governed by a variational–hemivariational inequality

History-dependent fractional hemivariational inequality with time-delay system for a class of new frictionless quasistatic contact problems

“…According to [6, 7], we denote by F 0 ( x ; v ) the Clarke generalized directional derivative of F at x in the direction v , that is…”

“…The mathematical theory of hemivariational and variational–hemivariational inequalities was first studied by Panagiotopoulos [1, 2]. Hemivariational inequalities can be used to describe various physical phenomena, which include nonconvex, nondifferentiable local Lipschitz functions, and have been considered extensively in a variety of mathematical theory analysis and engineering applications during the last 30 years, see [3–9] and the references therein. Recently, fractional hemivariational inequalities have attracted extensive attention and achieved good results in mathematical, physics and engineering research [10–14].…”

Calmness of the solution mapping of Navier-Stokes problems modeled by hemivariational inequalities

“…In the last years many papers about hemivariational inequalites similar to that of [1] and [2], with important applications, were published. As an example we mention only the quite recently appeared article [24]. Since the study of calmness of the solution sets for similar problems is undoubtely important, we will embed our problem in an abstract model of parametric equilibrium problem defined by trifunction and we will apply the abstract results obtained for the hemivariational inequalites governed by the Navier-Stokes operator, where the parameters are functions with some properties similar to those of Clarke generalized derivatives.…”

Impulsive hemivariational inequality for a class of history-dependent quasistatic frictional contact problems

“…Some classical results about contact problem can be found in several research papers and monographs, see [1,8,28,16,14] and the reference therein. Various classes of quasistatic contact problems for viscoelastic materials have been considered, we can refer to [34,30,17,20,18] and the references therein. Recently, variational inequalities with history-dependent operators were widely studied and applied to quasistatic contact problems, see [9,29,31,32,33,21,25,13,4].…”

“…We need to explain (5) and (6). At present, many people have studied the contact problem, which the contact surface is not affected by the impact, see [23,24,36,17] and the reference therein. Notice that few people studied the effect of impulse about the surface force f N .…”