TY - JOUR
T1 - On Higher-Order Generalized Emden-Fowler Differential Equations with Delay Argument
AU - Domoshnitsky, A.
AU - Koplatadze, R.
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - 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 ∈ Lloc(R+;R−), μ ∈ C(R+;(0,+∞)), τ ∈ C(R+;R+), τ(t) ≤ t for t ∈ R+ and limt→+∞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.
AB - 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 ∈ Lloc(R+;R−), μ ∈ C(R+;(0,+∞)), τ ∈ C(R+;R+), τ(t) ≤ t for t ∈ R+ and limt→+∞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.
UR - http://www.scopus.com/inward/record.url?scp=85028252358&partnerID=8YFLogxK
U2 - 10.1007/s10958-016-3195-1
DO - 10.1007/s10958-016-3195-1
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AN - SCOPUS:85028252358
SN - 1072-3374
VL - 220
SP - 461
EP - 482
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
IS - 4
ER -