Geodesic
On~solutions with generalized power asymptotics to systems of differential equations
Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 851-861

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In the paper we study methods for constructing particular solutions with nonexponential asymptotic behavior to a system of ordinary differential equations with infinitely differentiable right-hand sides. We construct the corresponding formal solutions in the form of generalized power series whose first terms are particular solutions to the so-called truncated system. We prove that these series are asymptotic expansions of real solutions to the complete system. We discuss the complex nature of the functions that are represented by these series in the analytic case. 
@article{MZM_1995_58_6_a4,
     author = {V. V. Kozlov and S. D. Furta},
     title = {On~solutions with generalized power asymptotics to systems of differential equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {851--861},
     publisher = {mathdoc},
     volume = {58},
     number = {6},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_6_a4/}
}
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V. V. Kozlov; S. D. Furta. On~solutions with generalized power asymptotics to systems of differential equations. Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 851-861. http://geodesic.mathdoc.fr/item/MZM_1995_58_6_a4/