The article discusses the existence and uniqueness of solutions in the broad sense of a first-order partial differential counting system that are periodic in some variables.

The study of periodic solutions of partial differential systems occupies a special place in the modern theory of differential equations. A wide variety of problems in mechanics, physics and technology come down to the study of oscillatory solutions of systems of differential equations, both ordinary and partial derivatives.

The article applies the method of characterization and establishes sufficient conditions for the existence and uniqueness of a periodic solution in a part of variables in the broad sense of a linear infinite system of first-order partial differential equations. Definitions of a solution in the broad sense of an infinite first-order partial differential system are given.