由强迫函数诱导的高阶泛函微分不等式的有界振动

Bounded Oscillations of Higher Order Functional Diffrential Inequalities Induced by Forcing Funcions

本文考虑了非线性泛函微分不等式Ｘ（ｔ）｛ＬｎＸ（ｔ）十ｆ（ｔ，ｘ（ｇ１（ｔ））），…Ｘ（ｇｍ（ｔ）））－ｈ（ｔ）｝≤０．（当ｎ为奇数时）（１）ｘ（ｔ）｛Ｌｎｘ（ｔ）－ｆ（ｔ，ｘ（ｇ１（ｔ）），…Ｘ（ｇｍ（ｔ）｝≥０（当ｎ为偶数时）（２）的振动问题，得到了不等式（１）和（２）的一切有界解振动和一切解振动的充分条件．

in this paper,we consider the problem of oscillations for the nonlinear functional differential inequalitiesx(t) {Lnx(t) + f(t,x(g1 )),...x(gm(t))-h(t)}≤ 0,when n is odd,(1)x(t) {Lnx(t)- f(t,x(g1)),...x(gm(t)- h(t))≥0,when n is even (2)sufficient conditions of oscillations for all bounded solutions and all solutions of inequalities (1)(or(2)) are obtained.