On Transformations Of Functional-Differential Equations

. The paper contains applications of Schroder's equation to differential equations with a deviating argument. There are derived conditions under which a considered equation with a deviating argument intersecting the identity y = x can be transformed into an equation with a deviation of the form ø(x) = x. Moreover, if the investigated equation is linear and homogeneous, we introduce a special form for such an equation. This special form may serve as a canonical form suitable for the investigation of oscillatory and asymptotic properties of the considered equation. 1. Introduction and notation In this article the transformations of functional-differential equations with one deviating argument are studied. These transformations are supposed to be global, i.e., they are defined on the whole definition intervals of corresponding equations. The case where the deviating argument of a considered equation is a sufficiently smooth function with a positive derivative and which does not intersect..