On a mathematical model of investment management leading to a system with constant and linear delays

A mathematical model for managing investments in advertising is proposed, in which all the factors that affect the process of delivering information are taken into account. In contrast to earlier models, various different ways of disseminating information are discussed. The model considered is described by differential equations that contain constant delay, linear delay, and impulse control. For systems of this type, the notion of a solution is formalized and a theorem of the existence of a solution is proved.