ON HIGHER-ORDER GENERALIZED EMDEN-FOWLER DIFFERENTIAL EQUATIONS WITH DELAY ARGUMENT

摘要

We consider a differential equation u~((n)(t)+p(t)|u(τ(t)|~(μ~(t))signu(τ(t)) = 0. It is assumed that n ≥ 3, p ∈ L_(loC)(R_+;R_-), μ ∈ C(R_+;(0, +oo)), 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.