In this paper, we consider and study a new class of hemivariational inequalities, which is called trifunction hemivariational inequality. We suggest and analyze a class of iterative methods for solving trifunction hemivariational inequalities using the auxiliary principle technique. We prove that the convergence of these new methods either requires partially relaxed strongly monotonicity or pse...

In the paper we present a survey on the mathematical modeling of nonconvex and nonsmooth problems arising in the mathematical theory of contact mechanics which is a growing field in engineering and scientific computing. The approach to such problems is based on the notion of hemivariational inequality and our presentation focuses on three aspects. First we present the ideas leading to inequalit...

We consider an elliptic hemivariational inequality with nonlocal nonlinearities. Assuming only certain growth conditions on the data, we are able to prove existence results for the problem under consideration. In particular, no continuity assumptions are imposed on the nonlocal term. The proofs rely on a combined use of recent results due to the authors on hemivariational inequalities and opera...

In this paper we study an inverse problem governed by a constrained nonlinear elliptic quasi-variational hemivariational inequality. The inequality involves two nondifferentiable functions which directly depend on solutions. We solve the direct and obtain properties of weak closedness uniform boundedness solutions, develops some existing results in literature. Then, using regularized optimizati...

Abstract In this paper we investigate a new class of elliptic variational–hemivariational inequalities without the relaxed monotonicity condition generalized subgradient. The inequality describes mathematical model steady state flow incompressible fluid Bingham type in bounded domain. boundary represents generalization no leak condition, and multivalued nonmonotone version nonlinear Navier–Fuji...

The goal of this paper is to study a mathematical model nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by combination Signorini unilateral frictionless condition, and nonmonotone multivalued contact, friction laws subdifferential form. First, under suitable assumptions, we deliver weak formulation model, which an elliptic system Lagrange m...

Abstract We study the Stokes problem for incompressible fluid with mixed nonlinear boundary conditions of subdifferential type. The latter involve a unilateral condition, Navier slip nonmonotone version Navier–Fujita and threshold leak condition frictional weak form leads to new class variational–hemivariational inequalities on convex sets velocity field. Solution existence compactness solution...

Abstract We study a nonlinear evolutionary quasi–variational–hemivariational inequality (in short, (QVHVI)) involving set-valued pseudo-monotone map. The central idea of our approach consists introducing parametric variational problem that defines selection associated with (QVHVI). prove the solvability by employing surjectivity theorem for sum operators, combined Minty’s formulation and techni...

Recently, in [Tang GJ, Cen JX, Nguyen VT, et al. Differential variational-hemivariational inequalities: existence, uniqueness, stability, and convergence. J Fixed Point Appl. 2020; DOI: 10.1007/s11784-020-00814-4],we studied a comprehensive system called differential variational-hemivar-iational inequality (DVHVI, for short) which is composed of nonlinear evolution equation time-dependent Banac...