非线性非自治中立型时滞差分方程线性化振动性

LINEARIZED OSCILLATIONS FOR THE FIRSTORDERNONLINEAR NONAUTONOMOUS NEUTRALDIFFERENCE EQUATIONS WITH DELAYS

考虑一阶非线性非自治中立型时滞差分方程△［ｘｎ－ｐｎｇ（ｘｎ－ｋ）］＋ｑｎ（ｘｎ－ｌ）＝０，（ｎ≥０）其中｛ｐｎ｝、｛ｑｎ｝是非负实数列，ｇ，ｈ∈Ｃ［Ｒ，Ｒ］，ｋ＞０，ｌ≥０是整数．本文证明了在一定条件下方程与其相应的线性化方程具有相同的振动性．

This paper discusses the firstorder nonlinear nonautonomaus neutral difference equation with delays of the form △[xn-png(xn-k)]+qnh(xn-l)=0where {pn},{qn} are sequences of nonnegative real numbers. g. h∈c,k>0,l≥0 are integers. It is proved that, under appropriate assumptions, the equation has the same oscillation with an assosiated linear equation.