On higher order generalized Emden-Fowler differential equations with delay argument - Domoshnitsky, A.; Koplatadze, R. (Нелінійні коливання, 2015)
In the paper the differential equation u⁽ⁿ⁾ (t) + p(t)|u(τ (t))|^(µ(t)) sign u(τ (t)) = 0, is considered. Here, we assume that n ≥ 3, p ∈ Lloc(R₊; R₋), µ ∈ C(R₊; (0, +∞)), τ ∈ C(R₊; R₊), τ (t) ≤ t for t ∈ R₊ and limt→+∞ τ (t) = +∞. In case µ(t) ≡ const > 0, oscillatory properties of equation have been extensively studied, where as if µ(t) ≢ const, to the extent of authors’ knowledge, the analogous questions have not been examined. In this paper, new sufficient conditions for the equation (∗) to have Property B are established.