A new Razumikhin theorem for delay difference equations
โ Scribed by Shunian Zhang; Ming-Po Chen
- Book ID
- 104353410
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 386 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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.
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, we consider the delay diff~ence equation Zn+l-Xn+Pnzn-k=O, n=0,1,2,..., where {p,) is a sequence of nonnegative real numbers and k is a positive integer. Some new results for the oscillation of this equation are obtained. Our theorems improve all known results in the literature. (~) 2