摘要
考虑具有振动系数的中立型时滞微分方程 [x(t)+p(t)x(t-τ(t) ) ]′ +Q(t)x(t-σ) =0 ,t≥ 0 ,其中p、Q∈C([0 ,∞ ) ,R) ,τ∈ (0 ,∞ ) ,σ∈ [0 ,+∞ ) ,Q(t)最终不恒为零。记Q+ (t) =max{ 0 ,Q(t) } ,Q-(t) =-min{ 0 ,Q(t) }。获得了该方程的每一个解或者振动或者趋于零的一个新的充分条件。
In this paper,the author considers neutral delay differential equation with oscillating coefficients [x(t)+p(t)· x(t-τ)]′+Q(t)x(t-σ)=0,t≥0, where Q、p∈c([0,∞),R),τ∈(0,∞),σ∈[0,∞),Q(t)0, eventually.Denote Q +(t)= max ｛0,Q(t)｝,Q -(t)=- min ｛0,Q(t)｝, the author obtains a new sufficient condition for the every solution of Eq(1)to oscillate or tend to zero.
