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nonlinear differential equations; $P_\omega (\lambda _0)$-solutions; asymptotic beaviour; regularly varying functions

References:

[1] Evtukhov, V.M.: **Asymptotic representations of solutions of nonautonomous ordinary differential equations**. Doctoral (Phys.-Math.) Dissertation, Kiev (1998).

[2] Evtukhov, V.M., Elshour, Mousa Jaber Abu: **Asymptotic behaviour of solutions of the nonautonomous ordinary differential $n$-th order equations**. Nonlinear Oscillations 19 (1) (2016), 22–31. MR 3669587

[3] Evtukhov, V.M., Samoilenko, A.M.: **Conditions for the existence of solutions of real nonautonomous systems of quasilinear differential equations vanishing at a singular point**. Ukrainian Math. J. 60 (1) (2010), 56–86. DOI 10.1007/s11253-010-0333-7 | MR 2888579 | Zbl 1224.35033

[4] Evtukhov, V.M., Samoilenko, A.M.: **Asymptotic representations of solutions of nonautonomous ordinary differential equations with regularly varying nonlinearities**. Differ. Uravn. 47 (5) (2011), 628–650. MR 2918280 | Zbl 1242.34092

[5] Kiguradze, I.T., Chanturia, T.A.: **Asymptotic properties of solutions of nonautonomous ordinary differential equations**. Kluwer Academic Publishers Group Dordrecht, 1993. MR 1220223 | Zbl 0782.34002

[6] Seneta, E.: **Regularly Varying Functions**. Berlin Springer-Verlag, 1976, Translated under the title Pravil'no menyayushchiesya funktsii, Moscow Nauka, 1985. MR 0815924 | Zbl 0324.26002