奇阶中立型微分方程的振动性

Oscillation of odd order neutral differential equations

考虑奇数阶中立型微分方程 dndtn[x(t) -P(t) x(t-τ) ]+ Q(t) x(t-σ) =0 ,t≥ t0 ,其中 P、Q∈ C([t0 ,∞ ) ,R+ ) ,以及τ、σ∈ R+ ,得到了方程所有解振动的充分条件 ,改进了文献 [1 ,2 ]的结果。

The odd order neutral differential equation d-n d t n[x(t)-P(t)x(t-τ)]+Q(t)x(t-σ)=0,t≥t 0 here P,Q∈ C ([t 0,∞),R +) and τ,σ∈R +,is discussed.The sufficient conditions of oscillation for all solutions to the equation are obtained.The results improve the results of references [1] and [2].