Stability of classical solutions of the Yang–Mills equations with source

N. N. Bogolyubov's strong coupling method is used to construct an expansion of the color charge operators with respect to a small parameter. The condition of stability with respect to small quantum fluctuations is formulated as the requirement that there should be no solutions of the Heisenberg equation that increase with time. It is shown that if the charge vector of the source is oriented in a definite direction in the color space, only solutions with complete screening will be stable.