Coercive and semicoercive hemivariational inequalities

In this paper, we consider the problem of the existence of anti-periodic solutions for quasilinear parabolic hemivariational inequalities with a pseudomonotone operator. Using regularized approximating and first eigenfunction methods and the surjectivity result, we prove the existence of solutions for quasilinear parabolic hemivariational inequalities.

In this paper, we extend the extremality results for the variational inequality to a higher order evolution hemivariational inequality. More precisely, we give an existence theorem of solution for the higher order evolution hemivariational inequality by using the sub–super-solution method. We prove the compactness of the solution set within an order interval formed by the sub-solution and super-solution. We also show an existence theorem of the extremal solution for the higher order evolution hemivariational inequality under consideration.

In this paper, we introduce and study a new class of generalized quasi-variational-like hemivariational inequalities with multi-valued $\eta$-pseudomonotone operators in Banach spaces. Some new existence theorems of solutions for this class of generalized quasi-variational-like hemivariational inequalities are proved. The results presented in this paper generalize and extend some known results.

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.

In the present paper, we generalize the sub–supersolution method for a class of higher order quasi-linear elliptic hemi-variational inequalities. Using the notion of sub and supersolution, we prove the existence, comparison, compactness and extremality results for the higher order quasi-linear elliptic hemi-variational inequality under considerations.

The purpose of this work is to present in a general framework the hybrid discretization of unilateral contact and friction conditions in elastostatics. A projection formulation is developed and used. An existence and uniqueness results for the solutions to the discretized problem is given in the general framework. Several numerical methods to solve the discretized problem are presented (Newton, SOR, fixed points, Uzawa) and compared in terms of the number of iterations and the robustness with respect to the value of the friction coefficient.