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

Neuman, František

Result. Math. 26, No. 3-4, 354-359 (1994).

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.

Keywords:

first order ordinary differential equations; equivalence classes

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