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Original Articles

On Asymptotic Classification of Solutions to Fourth-Order Differential Equations with Singular Power Nonlinearity

Pages 502-521 | Received 30 Oct 2015, Accepted 01 Jul 2016, Published online: 23 Jun 2016

References

  • I. V. Astashova. On asymptotic behavior of alternating solutions to certain non-linear differential equations of the third and fourth order. In Reports of extended session of a seminar of the I. N. Vekua Institute of Applied Mathematics, volume 3(3), pp. 9–12, Tbilisi, 1988. In Russian
  • I. V. Astashova. Application of dynamical systems to the study of asymptotic properties of solutions to nonlinear higher-order differential equations. Journal of Mathematical Sciences, 126(5):1361–1391, 2005. http://dx.doi.org/10.1007/PL00021970.
  • I. V. Astashova. Classification of solutions of fourth-order equations of the Emden–Fowler type. Differ. Equ., 44(6):881–882, 2008.
  • I. V. Astashova. Asymptotic classification of solutions to 3rd and 4th order Emden-Fowler type differential equations. In Proceeding of the International Conference. Euler International Mathematical Institute, volume 2 of Ordinary Differential Equations, pp. 9–12, St Petersburg, 2011. EIMI.
  • I. V. Astashova. 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, pp. 22–290, Moscow, 2012. UNITY-DANA.
  • I. V. Astashova. On asymptotic behavior of solutions to a fourth order nonlinear differential equation. In Mathematical Methods in Finance and Business Administration. Proceedings of the 1st WSEAS International Conference on Pure Mathematics (PUMA’14), pp. 32–41, Tenerife, 2014. WSEAS Press, ISBN:978-960-474-360-5.
  • I. V. Astashova and V. V. Rogachev. On the number of zeros of oscillating solutions of third- and fourth-order equations with power nonlinearity. Journal of mathematical sciences, 17:733–748, 2014.
  • M. Bartušek and Z. Došlá. Asymptotic problems for fourth-order nonlinear differential equations. Boundary Value Problems, 89, 2013. http://dx.doi.org/10.1186/1687-2770-2013-89.
  • P. Hartman. Ordinary Differential Equations. Wiley, New York, 1964.
  • I. T. Kiguradze and T. A. Chanturia. Asymptotic properties of solutions of nonautonomous ordinary differential equations, volume 89. Kluwer, Academic Publishers, Dordrecht-Boston-London, 1993. http://dx.doi.org/10.1007/978-94-011-1808-8.
  • V. A. Kondratiev. On oscillation of solutions to linear third- and fourth-order equations. Trudy MMO, 8:259–281, 1959. In Russian
  • T. Kusano and M. Naito. Nonlinear oscillation of fourth-order differential equations. Canad. J. Math., 28:840–852, 1976. http://dx.doi.org/10.4153/CJM-1976-081-0.
  • D. L. Lovelady. An oscillation criterion for a fourth-order integrally superlinear differential equation. Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Natur.(8), 58(4):531–536, 1975.
  • W. E. Taylor, Jr.: Oscillation criteria for certain nonlinear fourth order equations. Internat. J. Math., 6(3):551–557, 1983. http://dx.doi.org/10.1155/S0161171283000502.
  • P. Waltman. Oscillation criteria for third order nonlinear differential equations. Pacif. J. Math., 18(2):385–389, 1966. http://dx.doi.org/10.2140/pjm.1966.18.385.

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