This paper considers the delay difference equation where p n is a sequence of nonnegative real numbers and k is a positive integer. Some new oscillation criteria for this equation are obtained. Our theorems improve all known results in the literature.
Oscillation criteria for difference equations with unbounded delay
โ Scribed by B.G. Zhang; Chuan Jun Tian
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 441 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
โฆ Synopsis
consider the delay difference equation G&+1 -%I + Pnr,(,) = 0, 72 = 0, 1,2,
. , where T : N + Z is nondecreasing, 7(n) < n for ra E N and iimn--roo 7(n) = co, {p,} is a nonnegative sequence. Some oscillation criteria for this equation are obtained.
๐ SIMILAR VOLUMES
Xn+l-xn+~-~Pi(n)xn-kl =0, n = 0,1,2,..., (\*\*) i=1 where {Pn} and {pi(n)} are sequences of nonnegative real numbers and k and ki are positive integers. New oscillation criteria of the forms limsup Pn > a + C(a) n~oo for equation (\*) and rn n-t-k i limsupZ E pi(s) > 1 n~oo /=1 s=n for equation (\*\
In this paper, some new oscillation criteria are obtained for the first-order delay difference equation k k Xn+I-x,~+ (k+l)k+l xn\_kรทf(n,x,~\_l~,...,xn\_t~) =0, n=0,1,2,..., where k,/1,/2,..., ls are positive integer numbers, f is a function. Our results improve the known results in the literature.