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On asymptotic behavior of solutions of n-TH order Emden-Fowler differential equations with advanced argument

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Abstract

We study oscillatory properties of solutions of the Emden-Fowler type differential equation

$$ u^{(n)} (t) + p(t)|u(\sigma (t))|^\lambda signu(\sigma (t)) = 0, $$

where 0 < λ < 1, p ∈ L loc(ℝ+; ℝ), σ ∈ C(ℝ+; ℝ+) and σ(t) ≥ t for t ∈ ℝ+.

Sufficient (necessary and sufficient) conditions of new type for oscillation of solutions of the above equation are established.

Some results given in this paper generalize the results obtained in the paper by Kiguradze and Stavroulakis (1998).

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Authors and Affiliations

  1. Department of Mathematics of Tbilisi State University, University st. 2, Tbilisi, 0186, Georgia

    R. Koplatadze

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  1. R. Koplatadze
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Koplatadze, R. On asymptotic behavior of solutions of n-TH order Emden-Fowler differential equations with advanced argument. Czech Math J 60, 817–833 (2010). https://doi.org/10.1007/s10587-010-0051-1

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  • DOI: https://doi.org/10.1007/s10587-010-0051-1

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