具有积分小系数的一阶中立型方程的振动性

OSCILLATION OF FIRST ORDER NEUTRAL DIFFERENTIAL EQUATIONS WITH INTEGRALLY SMALL COEFFICIENTS

考虑一阶中立型微分方程其中τ，Ｐ，Ｒ∈Ｃ（［ｔ０，∞］，０≤τ（ｔ）≤τ０（０，∞），在没有条件的情况下，本文得到了几个新的充分条件。改进了Ｃｈｅｎ，Ｙｕ和Ｈｕａｎｇ（Ｊ．Ｍａｔｈ．Ａｎａｌ．Ａｐｐｌ．１８５（１９９４），２８８～３０１）及Ｙｕ，Ｗａｎｇ和Ｑｉａｎ（Ｂｕｌｌ．Ａｕｓｔｒａｌ．Ｍａｔｈ．Ｓｏｃ，１４５（１９９２），１９５～２００）的结果。

Conisider the first order neutral differential epuation(x(t)-R(t)x(t-r))+P(t)x(t-r(t))=0Where r,P,R ∈C([t0,∞ ), R+),r∈(0,∞)and 0≤r(t)≤r0∈(0,∞).We obtain several new sufficient conditions for the oscillation of the above equation without the restrictionwihch improve recent new results obtained by Chen,Yu and Huang (J.Math.Anal.Appl,185(1994),288～301)and Yu,Wang and Qian(Bull.Austral.Math.Soc,145 (1992),195～200).