# Existence conditions and asymptotics of a class of solutions of differential equations of the second order(in Russian)

Author
Odessa National Maritime University
Abstract
An asymptotic representations of some solutions for one class of nonlinear non-autonomous differential equations of the second order are established. We give necessary and also sufficient conditions of existence for these solutions.
Keywords
nonlinear equations; $P_\omega(Y_0,Y_1,\lambda_0)$-solutions; asymptotic representations
Reference
1. Seneta E. Regularly varying functions. – M.: Nauka, 1985. – 144 p. (in Russian)

2. Kiguradze I.T., Chanturia T.A. Asymtptotic properties of solutions of nonautonomous ordinary differential equations. – M.: Nauka, 1990. – 440 p. (in Russian)

3. Kostin A.V., Evtukhov V.M. Asymptotics of solutions of one nonlinear differential equation// Dokl. An SSSR. – 1976. – V.231, ¹5. – P. 1059–1062. (in Russian)

4. Evtukhov V.M. On some nonlinear differential equation of the second order// Dokl. AN SSSR. – 1977. – V.233, ¹4. – P. 531–534. (in Russian)

5. Evtukhov V.M. Asymptotic properties of solutions of nonatonomous differential equation of the second order of Emden-Fowler type. – Dis. ... kand. phis.-mat. nauk: 01.01.02, Odessa, 1980. – 154 p. (in Russian)

6. Evtukhov V.M. Asymptotic representations of solutions of one class nonlinear differential equation of the second order// Dokl. AN GSSR. – 1982. – V.106, ¹3. – P. 473–476. (in Russian)

7. Kostin A.V. On asymptotics of extendible solutions equation of Emden-Fowler type// Dokl. AN SSSR. – 1971. – V.200, ¹1. – P. 28–31. (in Russian)

8. Maric V., Tomic M. Asymptotic properties of solutions of the equation $y''=f(x)\Phi(y)$// Mathematische Zeitschrift. – 1976. – V.149. – P. 261–266.

9. Maric V., Regular variation and differential equations. – Lecture notes in mathematics 1726. Springer- Verlag, Berlin Heidelberg, 2000. – 128 p.

10. Talliaferro S.D. Asymptotic behavior of the solutions of the equation $y''=\Phi(t) f(y)$// SIAM J. Math. Anal. – 1981. – V.12, ¹6. – P. 47–59.

11. Evtukhov V.M., Belozerowa M.A. Asymptotic representations of solutions essential nonlinear nonautonomous differential equation of the second order// Ukr. mat. gur. – 2008. – V.60, ¹3. – P. 310–331. (in Russian)

12. Belozerowa M.A. Asymptotic properties of a class of solutions of essential nonlinear differential equations of the second oder// Mat. Stud. – 2008. – V.29, ¹1. – P. 52–62. (in Russian)

13. Evtukhov V.M., Belozerowa M.A. Asymptotic representations of solutions non-autonomous differential equations of the second order with non-linearities of more general kind of Emden-Fowler non-linearity type// Nelinijni koluvannja. – 2009. – V.12, ¹1. – P. 3–15. (in Russian)

14. Evtukhov V.M., Samojlenko A. Asymptotic representations of the solutions of the nonautonomous with regurlarly varying nonlinearities// Dif. Eq. – 2011. – V.47, ¹5. – P. 628–650. (in Russian)

15. Evtukhov V.M., Kusick L.I. Asymptotic representations of solutions of one class non-linear differential equations of the second order// Visn. Od. un-ty. Mat. i Mech. – 2009. – V.14, ¹20. – P. 57–74. (in Russian)
Pages
184-197
Volume
41
Issue
2
Year
2014
Journal
Matematychni Studii
Full text of paper
Table of content of issue