Solvability Of Two Classes Of Perturbed Variational Inequalities

In this dissertation, we mainly study the solvability of a class of perturbed variational inequality with constant as a perturbed direction and the solvability of a class of perturbed general variational inequality containing operators of type ql. This dissertation is divided into three chapters.In Chapter 1, we introduce some backgrounds of perturbed variational in-equalities.In Chapter 2, the solvability of a class of perturbed variational inequality with constant as a perturbed direction is investigated under certain coercivity conditions. Two main results are obtained. The coercivity condition assumed in the first result implies that the solution set of the perturbed variational inequality is nonempty and bounded, while the another coercivity condition in the second one shows that the solution set of the perturbed variational inequality is contained in a closed ball.In Chapter 3, we obtain an existence result of the solutions for general vari-ational inequalities problem with the involved mapping belonging to an operator of type ql, which was recently introduced by Laszlo. By the way, we present an open mapping theorem for the operator of type ql. As an application, the solvability analysis for the solution sets of this perturbed generalized variational inequality is established.