一类非线性中立型差分方程解的振动性

OSCILLATION FOR SOLUTIONS OF A TYPE OF NONLINEAR NEUTRAL DIFFERENCE EQUATIONS

本文我们证明了下列两个差分方程Δ（ｘｎ － ｘｎ－ ｋ）α＋ ｑｎｆ（ｘｎ－ Ｔ） ＝ ０Δ（Δｙｎ－ １）α＋ ｋ－ αｑｎｆ（ｙｎ） ＝ ０振动的等价性．其中ｑｎ０，ｋ，Ｔ为正整数，α为两奇数之商，ｆ∈Ｃ（Ｒ，Ｒ）是非减的并满足ｘｆ（ｘ）＞ ０（ｘ≠０）．获得了这些方程振动的一些充分条件．

In this paper,We prove the equivalent for the oscillation of the following difference equations Δ(x n-x n-k ) α+q nf(x n-T )=0andΔ(Δy n-1 ) α+k -α q nf(y n)=0where q n0,k,T are positive integers, α1 is any quotient of odd intergers, f∈C(R,R),f is nondecreasing,and xf(x)>0(x≠0) .Some sufficient Conditions for the oscillation of the difference equations are obtained.