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Functional-differential equation; singular case; transformation; canonical form
The paper contains applications of Schrőder’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 $\tau (x)=\lambda x$. 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.
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