On the stability of the solution in an optimal control problem for a Schrödinger equation

This research paper deals with the Frechet differentiability and necessary condition for optimality in a problem governed by the coefficient of a Schrödinger equation. In order to obtain a stabile solution by means of strong convergence of any minimizer, we have used a more regular space and considered second adjoint problem for obtaining the gradient of the cost functional. Proving the Lipschitz continuity, we have stated the necessary condition for optimal solution.