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We would like to study the solution stability of a parametric control problemgoverned by semilinear elliptic equations with a mixed state-controlconstraint, where the cost function is nonconvex and the admissible set isunbounded. The main goal of this paper is to give some sufficient conditionsunder which the solution map is upper semicontinuous and continuous withrespect to parameters.

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