Geodesic
Asymptotics of Bounded-at-Infinity Solutions of the Principal Resonance Equation
Matematičeskie zametki, Tome 78 (2005) no. 1, pp. 85-97

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We consider a system of six nonlinear differential equations obtained by averaging fast forced oscillations. The main result consist in the construction of the asymptotics at infinity for the general solution with bounded amplitudes. We show that the structure of asymptotic series depends on the parameters so that the coefficients of the series vary in jumps on the resonance set. 
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     author = {L. A. Kalyakin and Yu. Yu. Bagderina},
     title = {Asymptotics of {Bounded-at-Infinity} {Solutions} of the {Principal} {Resonance} {Equation}},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_1_a8/}
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L. A. Kalyakin; Yu. Yu. Bagderina. Asymptotics of Bounded-at-Infinity Solutions of the Principal Resonance Equation. Matematičeskie zametki, Tome 78 (2005) no. 1, pp. 85-97. http://geodesic.mathdoc.fr/item/MZM_2005_78_1_a8/