摘要
本文考察方程（ａ（ｔ）（ｘ）ｘ￣（＇２ｎ＋１））＇＋ｐ（ｔ）ｆ（ｘ（ｔ））＝０的振动性，得到了该方程在某种限制下有非振动解的充分必要条件，并由此得到了Ｈｉｌｌｅ－Ｗｉｎｔｎｅｒ型比较定理。
in this paper,the authors obtain a sufficient and necessary conditions for the exis-tence of nonoscillatory solution of nonlinear differential equations (a (t)(x)X'(2n+1) )' +p(t)f (x) =0, from which we obtain a Hille-Wintner type comparison theorem such that the results of refs[1～5]have been generalized and irnproved.
