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Keywords:
linear differential equations; global investigations; transformations
linear differential equations; global investigations; transformations
Summary:
A survey of investigations of linear differential equations from the point of view of transformations is described. These investigations started in the middle of the last century and continued till the present time. Essential step was done in the fifties by O. Borvka, who started global investigations of the second order equations.
References:
[1] O. Borůvka: Lineare Differentialtransformationen 2. Ordnung. VEB Verlag, Berlin 1967; extended English version: Linear Differential Transformations of the Second Order, English Universities Press, London 1973. MR 0463539
[2] J. Hadamard: Les équations différentielles. In: Encyclopédie Française, T.I., 1.76 - 10, Paris 1937. Zbl 0015.34803
[3] E. E. Kummer: De generali quadam aequatione differentiali tertii ordinis. Progr. Evang. Königl. Stadtgymnasium Liegnitz 1834 (reprinted in J. Reine Angew. Math. 100 (1887), 1-10).
[4] S. Lie, F. Engel: Theorie der Transformationgruppe. Teubner, Leipzig 1930.
[5] G. Mammana: Decomposizione delle espressioni differenziali lineari omogenee in prodotti di fattori simbolici e applicazione rellativa allo studio delle equazioni differenziali lineari. Math. Z. 33 (1931), 186-231. MR 1545209
[6] F. Neuman: Global Properties of Linear Ordinary Differential Equations. 334 pages, Mathematics and Its Applications, East European Series 52, Kluwer Academic Publishers (with Academia Praha) Dordrecht / Boston / London 1991, ISBN 0-7923-1269-4. MR 1192133 | Zbl 0784.34009
[7] G. Sansone: Studi sulle equazioni differenziali lineari omogenee di terzo ordine nel campo reale. Revista Mat. Fis. Teor. Tucuman 6(1948), 195-253. MR 0027404 | Zbl 0041.41903
[8] P. Stäckel: Über Transformationen von Differentialgleichungen. J. Reine Angew. Math. 111 (1893), 290-302.
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