Remark on transformations of linear differential and functional-differential equations. (English) Zbl 1057.34040

Summary: For linear differential and functional-differential equations of \(n\)th-order criteria of equivalence with respect to pointwise transformations are derived.


34C41 Equivalence and asymptotic equivalence of ordinary differential equations
34A30 Linear ordinary differential equations and systems
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34K06 Linear functional-differential equations
Full Text: DOI EuDML


[1] Borůvka, O.: Linear Differential Transformations of the Second Order. The English Univ. Press, London, 1971. · Zbl 0218.34005
[2] Čermák, J.: Continuous transformations of differential equations with delays. Georgian Math. J. 2 (1995), 1-8. · Zbl 0817.34036
[3] Neuman, F.: On transformations of differential equations and systems with deviating argument. Czechoslovak Math. J. 31(106) (1981), 87-90. · Zbl 0463.34051
[4] Neuman, F.: Simultaneous solutions of a system of Abel equations and differential equations with several delays. Czechoslovak Math. J. 32(107) (1982), 488-494. · Zbl 0524.34070
[5] Neuman, F.: Transformations and canonical forms of functional-differential equations. Proc. Roy. Soc. Edinburgh 115 A (1990), 349-357. · Zbl 0714.34108
[6] 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
[7] Neuman, F.: On equivalence of linear functional-differential equations. Results Math. 26 (1994), 354-359. · Zbl 0829.34054
[8] Tryhuk, V.: The most general transformation of homogeneous linear differential retarded equations of the \(n\)-th order. Math. Slovaca 33 (1983), 15-21. · Zbl 0514.34058
[9] Wilczynski, E.J.: Projective differential geometry of curves and ruled spaces. Teubner, Leipzig, . · JFM 37.0620.02
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.