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Corollaries from this theorem for even and odd

n

are also proved for

solutions defined near

+

[42].

This work was supported by the RFBR Grant (no. 11-01-00989).

REFERENCES

[1] Emden R. Gaskugeln. Leipzig, 1907.

[2] Zeldovich Ya.B., Blinnikov S.I., Shakura N.I. Physical foundations of the structure

and evolution of stars. Moscow, MSU Publ., 1981.

[3] Bellman R. Stability Theory of Solutions of Differential Equations (Russ. translation),

Moscow, 1954.

[4] Sansone J. Ordinary differential equations, vol. 2. Moscow, InLit Publ., 1954.

[5] Kiguradze I.T., Chanturia T.A. Asymptotic properties of solutions of nonautonomous

ordinary differential equations. Dordrecht–Boston–London Kluwer, Academic

Publishers, 1993.

[6] Astashova I.V., Filinovskii A.V., Kondratiev V.A., Muravei L.A. Some problems in

the qualitative theory of differential equations.

J. of Natural Geometry

. Jnan Bhawan.

London, 2003, vol. 23, no. 1–2, pp. 1–126.

[7] Astashova I.V. Qualitative properties of solutions to quasilinear ordinary differential

equations. In: Astashova I.V. (ed.) Qualitative Properties of Solutions to Differential

Equations and Related Topics of Spectral Analysis: scientific edition. Moscow,

UNITY-DANA Publ., 2012, pp. 22–290.

[8] Atkinson F.V. On second order nonlinear oscillations.

Pac. J. Math.

, 1955, vol. 5,

no. 1, pp. 643–647.

[9] Kiguradze I.T. Asymptotic properties of solutions of a nonlinear Emden – Fowler

type differential equation.

Izv. Akad. Nauk SSSR, Ser. Mat

. [Math. USSR–Izvestija],

1965, vol. 29, no. 5, pp. 965–986 (in Russ.).

[10]

Waltman P.

Oscillation criteria for third order nonlinear differential equations.

Pac.

J. Math.

, 1966, vol. 18, pp. 385–389.

[11] Kiguradze I.T. On monotone solutions of nonlinear ordinary

n

th-order differential

equations.

Izv. Akad. Nauk SSSR, Ser. Mat

. [Math. USSR-Izvestija], 1969, vol. 6,

pp. 1373–1398 (in Russ.).

[12] Kostin A.V. On asymptotic of non-extendable solutions to Emden – Fowler type

equations.

DAN SSSR

, 1971, vol. 200, no. 1, pp. 28–31 (in Russ.).

[13] Kusano T., Naito M. Nonlinear oscillation of fourth-order differential equations.

Canad. J. Math

., 1976, no. 28(4), pp. 840–852.

[14] Lovelady D.L. An oscillation criterion for a fourth-order integrally superlinear

differential equation.

Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Natur

., 1975,

vol. (8) 58 (4), pp. 531–536.

[15] Kondratiev V.A., Samovol V.S. On certain asymptotic properties of solutions to

equations of the Emden – Fowler type.

Differents. Uravn

. [Differential Equations],

1981, vol. 17, no. 4, pp. 749–750 (in Russ.).

[16] Kvinikadze G.G., Kiguradze I.T. On quickly growing solutions of nonlinear ordinary

differential equations.

Soobsh. Academy of Science GSSR

, 1982, vol. 106, no. 3,

pp. 465–468 (in Russ.).

[17] Taylor W.E. Jr. Oscillation criteria for certain nonlinear fourth order equations.

Internat. J. Math

. 1983, no. 6(3), pp. 551–557.

[18] Izobov N.A. On the Emden – Fowler equations with infinitely continuable solutions.

Mat. Zametki

[Mathematical Notes], 1984, vol. 35, iss. 2, pp. 189–199 (in Russ.).

[19] Kvinikadze G.G. On monotone regular and singular solutions of ordinary differential

equations.

Differents. Uravn

. [Differential Equations], 1984, vol. 20, no. 2, pp. 360–

361 (in Russ.).

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