About decisions of one system of equations that depend on parameter
In introduction the urgency of researches is defined and an object of research is determined as a system of equations which consists of two quasi-polynomials of a special type, that depends on small parameter <i>µ</i>, 0 ≤ <i>µ</i> << 1. A purpose of this article is to study structure and properties of a set of decisions of considered system. In the main part limiting properties of decisions of the system are revealed in case of <i>µ</i> → 0. Connection between system decisions in case of <i>µ</i> = 0 and small enough <i>µ</i> > 0 is established. Conditions on system parameters in case of which system has no decisions for any small enough <i>µ</i> > 0 are defined. Properties, which are sated, are like a basis of reason for a general approach to proof on the basis of a method of a state space of conditions of controllability (observability) in different functional spaces of the linear stationary singularly perturbed systems with delay and can be used for receiving and explanation of other structural properties of singularly perturbed manage-ment systems.