The asymptotic properties of the solutions of some third-order differential equation are examined. Sufficient conditions for the square integrability and oscillation of the solutions are established.
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R. P. Agarwal, S. R. Grace, and D. O’Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer, Dordrecht (2000).
L. Erbe, “Oscillation, nonoscillation, and asymptotic behavior for third-order nonlinear differential equations,” Ann. Mat. Pura Appl., 4, No. 110, 333–391 (1976).
M. Gera, J. R. Graef, and M. Greguˇs, “On oscillatory and asymptotic properties of solutions of certain nonlinear third-order differential equations,” Nonlin. Anal., 32, 417–425 (1998).
J. R. Graef and M. Remili, “Some properties of monotonic solutions of x′′′ + p(t)x′ + q(t) f(x),” PanAmer. Math. J., 22, 31–39 (2012).
J. R. Graef and M. Remili, “Oscillation criteria for third-order nonlinear differential equations,” Comm. Appl. Nonlin. Anal., 18, 21–28 (2011).
M. Greguš, Third-Order Linear Differential Equations, Reidel, Boston (1987).
M. Greguš and J. R. Graef, “On a certain nonautonomous nonlinear third-order differential equation,” Appl. Anal., 58, 175–185 (1995).
M. Greguš, J. R. Graef, and M. Gera, “Oscillating nonlinear third-order differential equations,” Nonlin. Anal., 28, 1611–1622 (1997).
J. W. Heidel, “Qualitative behavior of solutions of a third-order nonlinear differential equation,” Pacif. J. Math., 27, 507–526 (1968).
I. Kiguradze and T. Chanturia, Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Kluwer, Dordrecht (1993).
T. Kura, “Nonoscillation criteria for nonlinear ordinary differential equations of the third order,” Nonlin. Anal., 8, 369–379 (1984).
P. A. Ohme, “Asymptotic behavior of the solutions of the third-order nonlinear differential equations,” Ann. Mat. Pura Appl., 104, 43–65 (1975).
S. H. Saker, “Oscillation criteria of third-order nonlinear delay differential equations,” Math. Slovaca, 56, 433–450 (2006).
A. Škerlík, “Oscillation theorems for third-order nonlinear differential equations,” Math. Slovaca, 42, 471–484 (1992).
A. Tiryaki and M. F. Aktas, “Oscillation criteria of a certain class third-order nonlinear differential equations with damping,” J. Math. Anal. Appl., 325, 54–68 (2007).
P. Waltman, “Oscillation criteria for third-order nonlinear differential equations,” Pacif. J. Math., 18, 385–389 (1966).
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Published in Neliniini Kolyvannya, Vol. 20, No. 1, pp. 74–84, January–March, 2017.
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Graef, J.R., Remili, M. Asymptotic Behavior of the Solutions of a Third-Order Nonlinear Differential Equation. J Math Sci 229, 412–424 (2018). https://doi.org/10.1007/s10958-018-3686-3
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DOI: https://doi.org/10.1007/s10958-018-3686-3