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The paper presents an first type boundary value problem for a Schrödinger equation. The aim of paper is to give the existence and uniqueness theorems of the boundary value problem using Galerkin’s method. Also, a priori estimate for its solution is given.

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In this paper, an optimal control problem with final observation for systems governed by nonlinear time-dependent Schr?dinger equation is studied. The existence and uniqueness of the solution of considered optimal control problem are proved. The first variation of objective functional is obtained and a necessary optimality condition in the variational form is given.

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