向量似变分不等式解的存在性及解集的稳定性

本文首先得到一类广义向量似变分不等式问题的解的存在性定理,然后利用usco映射的性质,讨论广义向量似变分不等式的解集的通有稳定性,得到大多数(在Baire分类意义下)广义向量似变分不等式问题的解集是稳定的;另外还引入广义向量似变分不等式解集的本质连通区的概念,并证明了满足一定连续性、凸性条件的广义向量似变分不等式的解集至少存在一个本质连通区.

EXISTENCE AND STABILITY OF THE SOLUTIONS FOR VECTOR VARIATIONAL INEQUALITIES

In this paper, first, we obtain the existence theorem of the solutions for a class of generalized vector variational-like inequalities; second, by the usco mapping, we discuss the stability of the solution set of the generalized vector variational-like inequality, obtain that the solution set of most of the generalized vector variational-like inequalities (in the Baire category sense) is stable; and for any generalized vector variational-like inequality (satisfying some continuity and convexity conditions), there exists at least one essential connected component of the solution set.