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Asymptotics of Solutions of Nonautonomous Second-Order Ordinary Differential Equations Asymptotically Close to Linear Equations

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Ukrainian Mathematical Journal Aims and scope

Asymptotic representations are obtained for a broad class of monotone solutions of nonautonomous two-term second-order ordinary differential equations close in a certain sense to linear equations.

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References

  1. I. T. Kiguradze and T. A. Chanturiya, Asymptotic Properties of the Solutions of Nonautonomous Ordinary Differential Equations [in Russian], Nauka, Moscow (1990).

    Google Scholar 

  2. V. M. Evtukhov and Mousa Jaber Abu Elshour, “Asymptotic behavior of solutions of second-order nonlinear differential equations close to linear equations,” Mem. Different. Equat. Math. Phys., 43, 97–106 (2008).

  3. Mousa Jaber Abu-Elshour, “Asymptotics of solutions of nonautonomous second-order ordinary differential equations close to linear equations,” Nelin. Kolyvannya, 11, No. 2, 230–241 (2008); English translation: Nonlin. Oscillations, 11, No. 2, 242–254 (2008).

    Article  Google Scholar 

  4. Mousa Jaber Abu Elshour, “Asymptotic representations of the solutions of a class of the second-order nonautonomous differential equations,” Mem. Different. Equat. Math. Phys., 44, 59–68 (2008).

    Google Scholar 

  5. Mousa Jaber Abu Elshour and V. M. Evtukhov, “Asymptotic representations for solutions of a class of second-order nonlinear differential equations,” Miscolc Math. Notes, 2, 119–127 (2009).

    MathSciNet  Google Scholar 

  6. Mousa Jaber Abu Elshour, “Asymptotic representations of solutions of second-order nonlinear differential equations,” Int. Math. Forum, 4, No. 17, 835–844 (2009).

    MathSciNet  MATH  Google Scholar 

  7. E. Seneta, Regularly Varying Functions, Springer, Berlin (1976).

    Book  MATH  Google Scholar 

  8. V. M. Evtukhov, Asymptotic Representations of the Solutions of Ordinary Differential Equations [in Russian], Doctoral-Degree Thesis (Physics and Mathematics), Kiev (1998).

  9. 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).

    Article  MathSciNet  Google Scholar 

  10. V. M. Evtukhov and V. N. Shinkarenko, “Asymptotic representations of the solutions of two-term nonautonomous ordinary differential equations of order n with exponential nonlinearity,” Differents. Uravn., 44, No. 3, 308–322 (2008).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Mechnikov Odessa National University, Odessa, Ukraine

    V. M. Evtukhov

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  1. V. M. Evtukhov
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 10, pp. 1346–1364, October, 2012.

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Evtukhov, V.M. Asymptotics of Solutions of Nonautonomous Second-Order Ordinary Differential Equations Asymptotically Close to Linear Equations. Ukr Math J 64, 1531–1552 (2013). https://doi.org/10.1007/s11253-013-0733-6

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  • DOI: https://doi.org/10.1007/s11253-013-0733-6

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