Linear Differential Equations with Delay Depending Linearly Upon Argument

摘要

In this report is explained a sufficiently complete theory of linear differential equations with constant coefficients and delays of the argument, which appear to be linear functions of the argument. Discussed are analytical properties of solutions, their images according to Laplace, representation of solutions and their descriptions in form of definite series. Especially separated was a simple case when the delays are directly proportional to the argument. Greater attention was devoted to problems of stability of the solutions. The proposed theory can be, for example, used when investigating continuous control of escaping objects from distances, when the delay cannot be disregarded. (Author)