On equivalence of linear functional-differential equations
type: Item
instance of: scholarly article
title: On equivalence of linear functional-differential equations
zbMATH Open document ID: 0829.34054
DOI: 10.1007/BF03323059
author: František Neuman
published in: Results in Mathematics
publication date: 1996-01-17T00:00:00Z
review text: 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 \(p_0 \equiv 0\), \(k = 1\), \(p_1 = \text{const}\).
reviewed by: J. Šimša
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 39B62
zbMATH DE Number: 785181
zbMATH Keywords: first order ordinary differential equations
zbMATH Keywords: equivalence classes
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03323059
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description: scientific article; zbMATH DE number 785181