报告题目：Nonemptiness and compactness of solution sets of weakly homogeneous variational inequalities
摘要：Recently, Gowda and Sossa studied deeply weakly homogeneous variational inequalities, which contain the polynomial complementarity problem as a special case. A lot of good theoretical results were obtained; and one of important results is about the nonemptiness and compactness of the solution set of the concerned problem under the copositivity of the involved mapping and some additional conditions. In this note, we aim to generalize such a result. We obtain that the solution set of the weakly homogeneous variational inequality is nonempty and compact when the involved mapping is a generalized copositive mapping and some additional conditions are satisfied. Such a result is a really generalization of the corresponding one achieved by Gowda and Sossa in the sense that every condition we used is strictly weaker than the corresponding condition in their theorem besides one condition they used being removed. Moreover, we also obtain two related results which also generalize the corresponding ones for the polynomial complementarity problem.