An optimal control problem for two-dimensional Schrödinger equation

On the existence and uniqueness of the solution of an optimal control problem for Schrödinger equation

“…If we consider initial boundary value problem (3)-(6) then by means of the results on solvability of initial boundary value problem for Schrödinger equation, known from the paper [18], we can formulate the following statement: (11). Then the problem (3)-(6) has a unique solution as…”

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

“…With these researches the existence and uniqueness for the optimal control problems have been proved. But the stability of the solution could have not been guaranteed by minimizing the functional (5) on the set (6). Namely, instability often occurs in the manner that there are some minimizing sequences fv m g &V for the functional I a (v) such as…”

The Solvability of the Initial-Boundary Value Problems for a Nonlinear Schrodinger Equation with a Special Gradient Term

“…It should be noted that the initial-boundary value problems for the linear and nonlinear Schrödinger equations in various formulations were previously studied in detail in [1, 2, 4-8, 16, 18]. However, even for the linear Schrödinger equation with a special gradient term, initial-boundary value problems are poorly investigated [10,17]. In this paper, we study the questions of the existence and uniqueness of solutions of boundary value problems for the linear one-dimensional and two-dimensional Schrödinger equations with a special gradient term, where the coefficients are square integrable functions.…”