Upper semicontinuity of the solution map to a parametric boundary optimal control problem with unbounded constraint sets

We would like to study the solution stability of a parametric control problem governed by semilinear elliptic equations with a mixed state-control constraint, where the cost function is nonconvex and the admissible set is unbounded. The main goal of this paper is to give some sufficient conditions under which the solution map is upper semicontinuous and continuous with respect to parameters.Comment: 17 page