We consider a differential equation
It is assumed that n ≥ 3, p ∈ L loc(R +;R −), μ ∈ C(R +;(0,+∞)), τ ∈ C(R +;R +), τ(t) ≤ t for t ∈ R + and lim t→+∞ τ(t) = +∞. In the case μ(t) ≡ const > 0, the oscillatory properties of equation (*) are extensively studied, whereas for μ(t) ≢ const, to the best of authors’ knowledge, problems of this kind were not investigated at all. We also establish new sufficient conditions for the equation (*) to have Property B.
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I. Graef, R. Koplatadze, and G. Kvinikadze, “Nonlinear functional differential equations with Properties A and B,” J. Math. Anal. Appl. 306, No. 1, 136–160 (2005).
R. Koplatadze, “On oscillatory properties of solutions of generalized Emden–Fowler type differential equations,” Proc. Razmadze Math. Inst. 145, 117–121 (2007).
R. Koplatadze, “Quasilinear functional differential equations with property A,” J. Math. Anal. Appl. 330, No. 1, 483–510 (2007).
R. Koplatadze, “On asymptotic behavior of solutions of “almost linear” and essentially nonlinear differential equations,” Nonlin. Anal.: Theory, Methods and Appl. 71, No. 12, 396–400 (2009).
R. Koplatadze and E. Litsyn, “Oscillation criteria for higher order “almost linear” functional differential equation,” Funct. Different. Equat. 16, No. 3, 387–434 (2009).
R. Koplatadze, “On higher order functional differential equations with Property A,” Georg. Math. J. 11, No. 2, 307–336 (2004).
R. Koplatadze and T. Chanturia, On Oscillatory Properties of Differential Equations with Deviating Argument [in Russian], Tbilisi State Univ. Press, Tbilisi (1977).
G. S. Ladd, V. Lakshmikantham, and B. G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, Dekker, New York (1987).
R. Koplatadze, “On oscillatory properties of solutions of functional differential equations,” Mem. Different. Equat. Math. Phys. 3, 3–179 (1994).
Y. H. Erbe, Q. Kong, and B. G. Zhang, Oscillation Theory for Functional Differential Equations, Dekker, New York (1995).
R. P. Agarval, S. R. Grace, and D. O’Regan, Oscillation Theory for Second Order Linear, Half-Linear, Singular, and Sublinear Dynamic Equations, Kluwer Acad. Publ., Dordrecht (2002).
I. Kiguradze and I. Stavroulakis, “On the solutions of higher order Emden–Fowler advanced differential equations,” Appl. Anal. 70, 97–112 (1998).
R. Koplatadze, “On asymptotic behavior of solutions of nth order Emden–Fowler differential equations with advanced argument,” Czechoslovak Math. J. 60(135), No. 3, 817–833 (2010).
A. Domoshnitski and R. Koplatadze, “On asymptotic behavior of solutions of generalized Emden–Fowler differential equations with delay argument,” in: Abstr. Appl. Anal., Art. ID 168425 (2014).
M. K. Gramatikopoulos, R. Koplatadze, and G. Kvinikadze, “Linear functional differential equations with Property A,” J. Math. Anal. Appl. 284, No. 1, 294–314 (2003).
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Published in Neliniini Kolyvannya, Vol. 18, No. 4, pp. 507–526, October–December, 2015.
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Domoshnitsky, A., Koplatadze, R. On Higher-Order Generalized Emden-Fowler Differential Equations with Delay Argument. J Math Sci 220, 461–482 (2017). https://doi.org/10.1007/s10958-016-3195-1
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DOI: https://doi.org/10.1007/s10958-016-3195-1