On equivalence of linear functional-differential equations.(English)Zbl 0829.34054

The first order ordinary differential equations $$y'(x) = p_0 (x)y(x) + \sum ^k_{i = 1} p_i (x)y (\psi_i (x))$$ (with $$k$$ deviating arguments, $$k \geq 1$$ is fixed) are divided into equivalence classes by means of transformations $$x = h(t)$$ and $$z(t) = f(t) y(h(t))$$. The author deals with the classes that contains an equation with $$k$$ constant deviations $$\psi_i (x) = x - c_i$$. A criterion when two equations with constant deviations lie in the same class is established. This result is explicitly applied to the case $$p_0 \equiv 0$$, $$k = 1$$, $$p_1 = \text{const}$$.
Reviewer: J.Šimša (Brno)

MSC:

 34K05 General theory of functional-differential equations 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 39B12 Iteration theory, iterative and composite equations 39B62 Functional inequalities, including subadditivity, convexity, etc.
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References:

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