TY - JOUR
T1 - On asymptotic behavior of solutions of generalized emden-fowler differential equations with delay argument
AU - Domoshnitsky, Alexander
AU - Koplatadze, Roman
PY - 2014
Y1 - 2014
N2 - The following differential equation u(n) (t) + p (t) | u (σ (t)) |μ(t) sign u (σ(t)) = 0 is considered. Here p Lloc (R+; R+), C (R+; (0, + ∞)), σ C (R+; R+), σ (t) ≤ t, and lim t → + ∞ σ(t) = + ∞. We say that the equation is almost linear if the condition lim t → + ∞ (t) = 1 is fulfilled, while if lim sup t → + ∞ (t) ≠ 1 or lim inf t → + ∞ (t) ≠ 1, then the equation is an essentially nonlinear differential equation. In the case of almost linear and essentially nonlinear differential equations with advanced argument, oscillatory properties have been extensively studied, but there are no results on delay equations of this sort. In this paper, new sufficient conditions implying Property A for delay Emden-Fowler equations are obtained.
AB - The following differential equation u(n) (t) + p (t) | u (σ (t)) |μ(t) sign u (σ(t)) = 0 is considered. Here p Lloc (R+; R+), C (R+; (0, + ∞)), σ C (R+; R+), σ (t) ≤ t, and lim t → + ∞ σ(t) = + ∞. We say that the equation is almost linear if the condition lim t → + ∞ (t) = 1 is fulfilled, while if lim sup t → + ∞ (t) ≠ 1 or lim inf t → + ∞ (t) ≠ 1, then the equation is an essentially nonlinear differential equation. In the case of almost linear and essentially nonlinear differential equations with advanced argument, oscillatory properties have been extensively studied, but there are no results on delay equations of this sort. In this paper, new sufficient conditions implying Property A for delay Emden-Fowler equations are obtained.
UR - http://www.scopus.com/inward/record.url?scp=84893761749&partnerID=8YFLogxK
U2 - 10.1155/2014/168425
DO - 10.1155/2014/168425
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AN - SCOPUS:84893761749
SN - 1085-3375
VL - 2014
JO - Abstract and Applied Analysis
JF - Abstract and Applied Analysis
M1 - 168425
ER -