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

0.2 Preliminaries

Let

Definition 2.1 Let . A function , with continuous coordinates satisfying initial conditions , , is said to be solution of system (0.1.4) if is differentiable almost everywhere on and satisfies almost everywhere on the system (0.1.4).
It is obvious that for the matrices

we have

(0.2.1)
Also, it is not difficult to verify that, for these matrices, the following statement is true.

Property 2.1. For the matrix , the following relations hold

1.

2.


3.

where .

We establish of the inequality in iii. Indeed, for , , we have










We use the statements in this Property 2.1. to prove the main result of this paper.