Statement and Solution of Boundary Problems for Infinite Systems of Ordinary Differential Equations
The author considers the problem of finding a solution of the infinite system of ordinary differential equations. The stated problem will be called the boundary problem for the infinite system of ordinary differential equations. On the basis of Picard's method of successive approximations, the author proves the theorem of the existence and singularity of the solution of the stated problem. The properties of the solution of the problem are established, as well as the conditions on satisfaction of which the solution of the boundary problem for an infinite system of differential equations (1) is reduced to the solution of such a problem for a finite system of differential equations.
Citation Example: Zhautykov O. A. Statement and Solution of Boundary Problems for Infinite Systems of Ordinary Differential Equations // Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 157 - 164.