On Higher-Order Generalized Emden-Fowler Differential Equations with Delay Argument

We consider a differential equationu(n)(t)+p(t)|u(τ(t))|μ(t)sign(τ(t))=0. 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.