广义拟变分不等式解集的稳定性及本质连通区的存在性

THE STABILITY AND THE EXISTENCE OF ESSENTIAL COMPONENTS OF THE SOLUTION SETS FOR GENERALIIED QUASI-VARIATIONAL INEQUALITIES

在赋范线性空间下,讨论广义拟变分不等式解集的稳定性,证明了满足一定连续性和凸性条件的广义拟变分不等式问题构成的空间M中,大多数(在Baire分类意义下)广义拟变分不等式问题的解集是稳定的,并证明了M中每一个广义拟变分不等式的解集至少存在一个本质连通区。

This paper studies the stability of the solution sets for generalized quasi-variational inequality problems.It prove that ,in the space M consisting of generalized quasi-variational inequality problems satisfying some convexity and continuity conditions, most generalized quasi-variational inequality problems(in the sense of Baire category) have stable solutions sets, and that for each problem in M, it's solution set possesses at least one essential component.