具有无界时滞微分方程解的振动性

OSCILLATORY PROPERTIES OF SOLUTIONS FOR DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAYS

考虑具有ｎ个变时滞的泛函微分方程ｘ′（ｔ）＋ｎｉ＝１ｑｉ（ｔ）ｘ（ｔ－σｉ（ｔ）），ｔ≥ｔ０，其中ｑｉ（ｔ），σｉ（ｔ）∈Ｃ（［ｔ０，∞），（０，∞）），ｉ＝１，２，…，ｎ．在时滞σｉ（ｔ）（ｉ＝１，２，…。

Consider the differential equatin with delayx′(t)+ni=1q i(t)x(t-σ i(t))=0,t≥t 0,where q i(t),σ i(t)∈C([t 0,∞),(0,∞)),i= 1,2,… ,n. In this paper, the Hunt_Yorke theorem and conjecture are proved when σ i(t)(i =1,2,…, n ) are unbounded. These results generalize the conclusions in and , and improve the corresponding results in .