Journal of Mathematical Sciences

, Volume 238, Issue 3, pp 316–332 | Cite as

Asymptotic Representations for the Solutions of Second-Order Differential Equations with Rapidly and Regularly Varying Nonlinearities

  • O. O. Chepok

We determine asymptotic representations for the solutions of one class of second-order differential equations with rapidly and regularly varying nonlinearities.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. M. Evtukhov and N. G. Drik, “ Asymptotic behavior of solutions of a second-order nonlinear differential equation,” Georg. Math. J., 3, No. 2, 123–151 (1996).MathSciNetzbMATHGoogle Scholar
  2. 2.
    V. M. Evtukhov and V. M. Kharkov, “Asymptotic representation of solutions of essentially nonlinear differential equations of second order,” Differents. Uravn., 43, No. 10, 1311–1323 (2007).zbMATHGoogle Scholar
  3. 3.
    E. Seneta, Regularly Varying Functions [Russian translation], Nauka, Moscow (1985).Google Scholar
  4. 4.
    V. Maric, Regular Variation and Differential Equations, Springer Science & Business Media, Berlin (2000).CrossRefzbMATHGoogle Scholar
  5. 5.
    N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation, Cambridge Univ. Press, Cambridge (1987).CrossRefzbMATHGoogle Scholar
  6. 6.
    V. M. Evtukhov and A. M. Klopot, “Asymptotic behavior of solutions of ordinary differential equations of order n with regularly varying nonlinearities,” Differents. Uravn., 50, No. 5, 584–600 (2014).zbMATHGoogle Scholar
  7. 7.
    V. M. Evtukhov and A. M. Samoilenko, “Conditions for the existence of solutions of real nonautonomous systems of quasilinear differential equations vanishing at a singular point,” Ukr. Mat. Zh., 62, No. 1, 52–80 (2010); English translation: Ukr. Math. J., 62, No. 1, 56–86 (2010).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • O. O. Chepok
    • 1
  1. 1.Mechnikov Odessa National UniversityOdessaUkraine

Personalised recommendations