Periodic Solutions by Picard's Approximations
Canadian mathematical bulletin, Tome 11 (1968) no. 5, pp. 743-745
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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
@article{10_4153_CMB_1968_092_2,
author = {Burton, T.A.},
title = {Periodic {Solutions} by {Picard's} {Approximations}},
journal = {Canadian mathematical bulletin},
pages = {743--745},
year = {1968},
volume = {11},
number = {5},
doi = {10.4153/CMB-1968-092-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-092-2/}
}
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