拟变分不等式解集的极小本质集及应用

Minimal essential set of the solution set of quasi-variational inequality and its applications

引入了拟变分不等式解集的极小本质集的概念,并证明了每个拟变分不等式(满足一定条件)的解集至少存在一个极小本质集.作为应用,还证明了大多数(在Baire分类意义下)拟-似变分不等式问题的解集是稳定的;每个拟-似变分不等式(满足一定条件)的解集至少存在一个本质连通区.

The paper introduces the concept of minimal essential set of the solution set of quasi-variational inequality,and it is proved that there exists at least one minimal essential set of the solution set for every quasi-variational inequality (satisfying some conditions).As a consequence,it deduces that the solution sets of most quasi-variational-like inequalities (in the Baire category sense) are stable;and for any quasi-variational-like inequality (satisfying some conditions) there exists at least one essential connected component of the solution set.