Degree Theory and Solution Existence of Set-Valued Vector Variational Inequalities in Reflexive Banach Spaces

In this paper, a degree theory for set-valued vector variational inequalities is built in reflexive Banach spaces. By using the method of degree theory, some existence results of solutions for set-valued vector variational inequalities are established under suitable conditions. Furthermore, some equivalent characterizations for the nonemptiness and boundedness of solution sets to single-valued vector variational inequalities are obtained under pseudomonotonicity assumption. To the best of our knowledge, there are still no papers dealing with the degree theory for vector variational inequalities.