Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 10, pp. 1-15.
Title: Oscillation criteria for delay difference equations
Authors: Jianhua Shen (Hunan Normal Univ., China)
I. P. Stavroulakis (Univ. of Ioannina, Greece)
Abstract:
This paper is concerned with the oscillation of
all solutions of the delay difference equation
$$ x_{n+1}-x_n+p_nx_{n-k}=0, \quad n=0,1,2,\dots $$
where $\{p_n\}$ is a sequence of nonnegative real numbers and $k$ is a
positive integer. Some new oscillation conditions are established. These
conditions concern the case when none
of the well-known oscillation conditions
$$ \limsup_{n\to \infty}\sum_{i=0}^kp_{n-i}>1 \quad{\rm and}\quad
\liminf_{n\to \infty}\frac{1}{k}\sum_{i=1}^kp_{n-i}>\frac{k^k}{(k+1)^{k+1}}
$$
is satisfied.
Submitted January 9, 2001. Published January 23, 2001.
Math Subject Classifications: 39A10.
Key Words: Oscillation; non-oscillation; delay difference equation.