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

Author
L. I. Kusick
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
pdf
Table of content of issue