Geodesic
Cauchy problem for the Mathieu equation away from parametric resonance
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1419-1433 
A. F. Kurin. Cauchy problem for the Mathieu equation away from parametric resonance. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1419-1433. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a5/
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     title = {Cauchy problem for the {Mathieu} equation away from parametric resonance},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Four solutions of the Cauchy problem for Mathieu’s equation away from parametric resonance domains are analytically constructed using an asymptotic averaging method in the fourth approximation. Three solutions occur near fractional parameter values at which slow combination phases exist. The fourth solution occurs in the absence of slow phases away from parametric resonance domains and the fractional parameter values.

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