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Criterion of global equivalence of linear differential equations

Published online by Cambridge University Press:  14 November 2011

František Neuman
František Neuman
Affiliation:
Mathematics Institute, Czechoslovak Academy of Sciences, Mendelovo nám. 1, 60300 Brno, Czechoslovakia
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Synopsis

A criterion of global equivalence of linear homogeneous differential equations of the n-th order, n ≧ 3, is derived, which is in general effective, i.e. expressible in terms of coefficients and quadratures.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 217 - 221
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Birkhoff, G. D.. On the solutions of ordinary linear homogeneous differential equations of the third order. Ann. Math. 12 (1910/1911), 103–124.CrossRefGoogle Scholar
2Borůvka, O.. Linear Differential Transformations of the Second Order (London: The English Univ. Press, 1971).Google Scholar
3Borůvka, O.. Teorija global'nych svojstv obyknovennych linějnych differencial'nych uravnenij vtorogo porjadka. Differencial'nyje Uravněnija 12 (1976), 1347–1383.Google Scholar
4Everitt, W. N.. On the transformation theory of ordinary second order linear symmetric differential equations. Czechoslovak Math. J. 32 (107) 1982, 275–306.CrossRefGoogle Scholar
5Halphen, G. H.. Mémoire sur la réduction des équations différentielles linéaires aux formes intégrables. Mémoires présentés par divers savants à l'académie des sciences de l'institut de France 28 (1884), 1–301.Google Scholar
6Hustý, Z.. Die Iteration homogener linearer Differentialgleichungen. Publ. Fac. Sci. Univ. J. E. Purkyně (Brno) 449 (1964), 23–56.Google Scholar
7Kummer, E. E.. De senerali quadam aequatione differentiali tertii ordinis. Progr. Evang. Königl. Stadtgymnasiums Liegnitz 1834 (also: Crelles J. 100 (1887), 1–10).Google Scholar
8Neuman, F.. A survey of global properties of linear differential equations of the n-th order. Proceedings of the Conference on Differential Equations in Dundee 1982. Lecture Notes in Mathematics 964, 548–563 (Berlin: Springer, 1982).Google Scholar
9Stäckel, P.. Über Transformationen von Differentialgleichungen. Crelles J. 111 (1893), 290–302.CrossRefGoogle Scholar