Geodesic
Periodic Solutions by Picard's Approximations
Canadian mathematical bulletin, Tome 11 (1968) no. 5, pp. 743-745

Voir la notice de l'article provenant de la source Cambridge University Press

In [1] Demidovic considered a system of linear differential equations with A(t) continuous, T-periodic, odd, and skew symmetric. He proved that all solutions of (1) are either T-periodic or 2T-periodic0 In [2] Epstein used Floquet theory to prove that all solutions of (1) are T-periodic without the skew symmetric hypothesis. Epstein's results were then generalized by Muldowney in [7] using Floquet theory. Much of the above work can also be interpreted as being part of the general framework of autosynartetic systems discussed by Lewis in [5] and [6]. According to private correspondence with Lewis it seems that he was aware of these results well before they were published. However, it appears that these theorems were neither stated nor suggested in the papers by Lewis. 
Burton, T.A. Periodic Solutions by Picard's Approximations. Canadian mathematical bulletin, Tome 11 (1968) no. 5, pp. 743-745. doi: 10.4153/CMB-1968-092-2
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[1] 1. Demidovic, B.P., Moskov. Gos. Univ. UČ. Zap. 6 (1952) 123-132. Google Scholar

[2] 2. Epstein, I.J., Periodic solutions of systems of differential equations. Proc. Amer. Math. Soc. 13 (1962) 690-694. Google Scholar

[3] 3. Hurewicz, W., Lectures on ordinary differential equations. (Wiley, New York, 1958). Google Scholar

[4] 4. Lefschetz, S., Differential equations: geometric theory. (Interscience, New York, 1957). Google Scholar

[5] 5. Lewis, D.C., Autosynartetic solutions of differential equations Amer. J. Math. 83 (1961) 1-32. Google Scholar

[6] 6. Lewis, D. C., Int. Sym. nonlinear differential equations and nonlinear mechanics (Edited by LaSalle, J. P. and Lefschetz, S.). (Academic Press, New York, 1963) 99-104. Google Scholar

[7] 7. Muldowney, J. S., Linear systems of differential equations with periodic solutions. Proc. Amer. Math. Soc. 18 (1967) 22-27. Google Scholar

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