Resolvability of the optimum control problem for the ordinary differential equation of the second order with the Lions criterion of quality

The work is devoted to the study of a problem of optimum control for ordinary differential equations of the second order with the Lions functional as a criterion of quality. The correctness of the problem of optimum control for ordinary differential equations of the second order is investigated and the theorems of existence and uniqueness for the solution of the problem of optimum control are proved.