Neuman, František On equivalence of linear functional-differential equations. (English) Zbl 0829.34054 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) Cited in 11 Documents 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 PDF BibTeX XML Cite \textit{F. Neuman}, Result. Math. 26, No. 3--4, 354--359 (1994; Zbl 0829.34054) Full Text: DOI OpenURL References: [1] Aczél, J., Lectures on Functional Equations and Their Applications, Acad. Press, New York-London, 1966. · Zbl 0139.09301 [2] Blanton, G. and Baker, J. A., Iteration groups generated by Cn functions, Arch. Math. (Brno) 19 (1982), 121–127. · Zbl 0518.26002 [3] O. Boruvka, Linear Differential Transformations of the Second Order, The English Univ. Press, London, 1971. · Zbl 0222.34002 [4] Čermák, J., On transformations of functional-differential equations, Arch. Math. (Brno), to appear. [5] Čermák, J., Continuous transformations of differential equations with delays, Proc. Georg. Acad. Sci. Math., to appear. · Zbl 0817.34036 [6] Čermák, J., Note on simultaneous solutions of a system of Schröder equations, sent to Math. Bohemica. [7] Kuczma, M., Choczewski, B. and Ger, R., Iterative Functional Equations, Cambridge Univ. Press, Cambridge-New York, 1989. · Zbl 0703.39005 [8] Neuman, F., On transformations of differential equations and systems with deviating argument, Czechoslovak Math. J. 31 (106) (1981), 87–90. · Zbl 0463.34051 [9] Neuman, F., Simultaneous solutions of a system of Abel equations and differential equations with several deviations, Czechoslovak Math. J. 32 (107) (1982), 488–494. · Zbl 0524.34070 [10] Neuman, F., Transformations and canonical forms of functional-differential equations, Proc. Roy. Soc. Edinburgh 115 A (1990), 349–357. · Zbl 0714.34108 [11] Neuman, F., Global Properties of Linear Ordinary Differential Equations, Mathematics and Its Applications (East European Series) 52, Kluwer Acad. Publ., Dordrecht-Boston-London, 1991. · Zbl 0784.34009 [12] Tryhuk, V., The most general transformation of homogeneous linear differential retarded equations of the first order, Arch. Math. (Brno) 16 (1980), 225–230. · Zbl 0448.34073 [13] Zdun, M. C., On simultaneous Abel equations, Aequationes Math. 38 (1989), 163–177. · Zbl 0686.39009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.