Approximate controllability for a class of hemivariational inequalities

In this paper, we deal with the approximate controllability for control systems described by a class of hemivariational inequalities. Firstly, we introduce the concept of mild solutions for hemivariational inequalities. Then the approximate controllability is formulated and proved by utilizing a fixed-point theorem of multivalued maps and properties of generalized Clarke subdifferential.     

A multiplicity result for hemivariational inequalities

In this paper we extend a multiplicity result of Ricceri to locally Lipschitz functionals and prove the existence of multiple solutions for a class of hemivariational inequalities.     

Minimization principles for elliptic hemivariational inequalities

In this paper, we explore conditions under which certain elliptic hemivariational inequalities permit equivalent minimization principles. It is shown that for an elliptic variational–hemivariational inequality, under the usual assumptions that guarantee the solution existence and uniqueness, if an additional condition is satisfied, the solution of the variational–hemivariational inequality is also the minimizer of a corresponding energy functional. Then, two variants of the equivalence result are given, that are more convenient to use for applications in contact mechanics and in numerical analysis of the variational–hemivariational inequality. When the convex terms are dropped, the results on the elliptic variational–hemivariational inequalities are reduced to that on “pure” elliptic hemivariational inequalities. Finally, two representative examples from contact mechanics are discussed to illustrate application of the theoretical results.     

Multiple solutions for a class of elliptic hemivariational inequalities

The existence of multiple solutions to elliptic hemivariational inequality problems in bounded domains is investigated via a suitable nonsmooth version of a classical technique due to Struwe and a recent saddle point theorem for locally Lipschitz continuous functionals.     

Existence and approximated results of solutions for a class of nonlocal elliptic variational-hemivariational inequalities

In this paper, we consider the regularization of a class of elliptic variational-hemivariational inequalities driven by the fractional Laplace operator. First, we demonstrate characterizations of nonlocal elliptic variational-hemivariational inequalities. Next, we provide coercivity conditions that guarantee the existence and uniqueness of solution. Finally, by virtue of the so-called Browder–Tikhonov regularization method, we introduce a strongly convergent approximation procedure for the considered nonlocal problems considered without any coercivity condition.     

On double degenerate quasilinear parabolic variational inequalities

We deal with the existence of weak solutions of double degenerate quasilinear parabolic inequalities with a Signorini-Dirichlet-Neumann type mixed boundary condition, which may degenerate in certain subset of the boundary or on a segment in the interior of the domain and in time. The main tools in our study are the maximM monotone property of the derivative operator with zero-initial valued conditions and the theory of pseudomonotone perturbations of maximal monotone mappings.     

Existence of solutions for wave-type hemivariational inequalities with noncoercive viscosity damping

In this paper we prove the existence of solutions for a hyperbolic hemivariational inequality of the form

u″+Au′+Bu+∂j(u)∋f,     

On constrained hemivariational inequalities and their approximation

We prove the existence of a solution of a constrained hemivariational inequality, and, develop a fully discrete approximation of it. The relation between the constrained hemivariational inequality and a problem of finding substationary points of the corresponding potential function is also studied.     

拟线性椭圆型H-半变分不等式

本文研究一类拟线性椭圆型H-半变分不等式,即研究具有非凸、非光滑泛函的椭圆型不等式。这类问题的研究来自力学。利用Clarke广义梯度和伪单调算子理论,我们证明了拟线性椭圆型H-半变分不等式解的存在性。     

A minimax approach to semicoercive hemivariational inequalities

A new minimax approach for treating semicoercive hemivariational inequalities is presented. An elliptic Dirichlet problem at resonance and with discontinuous nonlinearties is solved under a recession condition     

Some uniqueness results for a class of quasilinear elliptic eigenvalue problems

Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in aN-ball or an annulus without monotone assumptions on the nonlinear termf. It is also proved that there is no non-radial positive solution. Supported by the Youth Foundations of National Education Commuttee and the Committee on Science and Technology of Henan Province     

On stably quasimonotone hemivariational inequalities

We establish some existence results for variational-hemivariational inequalities of the Hartman-Stampacchia type involving stably quasimonotone set-valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive a sufficient condition for the existence and boundedness of solutions.     

Weak Galerkin finite element method for a class of quasilinear elliptic problems

The purpose of this paper is to study the weak Galerkin finite element method for a class of quasilinear elliptic problems. The weak Galerkin finite element scheme is proved to have a unique solution with the assumption that guarantees the corresponding operator to be strongly monotone and Lipschitz-continuous. An optimal error estimate in a mesh-dependent energy norm is established. Some numerical results are presented to confirm the theoretical analysis.     

Multiplicity of solutions for a class of nonsymmetric eigenvalue hemivariational inequalities

The aim of this paper is to establish the influence of a non-symmetric perturbation for a symmetric hemivariational eigenvalue inequality with constraints. The original problem was studied by Motreanu and Panagiotopoulos who deduced the existence of infinitely many solutions for the symmetric case. In this paper it is shown that the number of solutions of the perturbed problem becomes larger and larger if the perturbation tends to zero with respect to a natural topology. Results of this type in the case of semilinear equations have been obtained in [1] Ambrosetti, A. (1974), A perturbation theorem for superlinear boundary value problems, Math. Res. Center, Univ. Wisconsin-Madison, Tech. Sum. Report 1446; and [2] Bahri, A. and Berestycki, H. (1981), A perturbation method in critical point theory and applications, Trans. Am. Math. Soc. 267, 1–32; for perturbations depending only on the argument.     

Existence of antiperiodic solutions for hemivariational inequalities

In this paper we consider the problem of existence of antiperiodic solutions for first-order and second-order hemivariational inequalities with a pseudomonotone operator. We first give the surjectivity result and then prove a existence of antiperiodic solutions for hemivariational inequalities with the surjectivity result.     

Periodic solutions to history-dependent differential hemivariational inequalities with applications

In this article, we investigate a hybrid model combined by a parabolic differential equation and a parabolic hemivariational inequality (so-called differential hemivariational inequality of parabolic–parabolic type) in general infinite dimensional spaces which includes the history-dependent operator. The solvability of initial value problems as well as the periodic problems of the hemivariational inequality and the differential hemivariational inequality have been proved. In application, we study a contact problem with normal compliance driven by a history-dependent dynamical system.     

Existence results for hemivariational inequalities with measures

We prove existence results for multivalued quasilinear elliptic problems of hemivariational inequality type with measure data right-hand sides. In case of L ¹-data, we study existence and enclosure behaviors of solutions by an appropriate sub-supersolution approach. The proofs of our results are based on general existence theory for multivalued pseudomonotone operators, and approximation-, truncation-, and special test function techniques.