Abstract
We investigate the optimal bilinear control problem governed by the coupled nonlinear Schrödinger systems with Coulombian potential in R3. The existence of the optimal control with initial data in H1 is presented by weak convergence method, and the Fréchet-differentiability of the objective functional with respect to the control is obtained based on H2 regularity. Furthermore, the first-order optimality system is rigorously derived. Our results have improved some recent works.
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