Infinite system of 2-systems of differential equations in Hilbert space Ibragimov G. I., Qushaqov H. Sh. Abstract

0.4 Conclusion

In this paper, a theorem on the existence and uniqueness of the solution of an infinite system of 2-systems of differential equations (0.1.4) in Hilbert space has been proved. We can write the infinite system in the form

where the infinite matrix is a block diagonal matrix consisted of matrices

This system of differential equations has been studied in this paper for the first time. We have proved the existence and uniqueness of the solution of an infinite system of 2-systems in the space . Clearly, is of the form of a Jordan block.

In the papers [13], [2] matrix in the following form was studied

and in [8] the case where

was studied, before. Then, control and differential game problems were studied based on the existence and uniqueness theorem infinite system. Such problems can be now studied for the infinite 2-systems (0.1.4) in the cases of integral and geometric constraints on controls of players. Therefore, the main result of the present paper is interesting for the researchers who do research on control or differential game problems for infinite system of differential equations.