In this study, a new companion transformation is used for the neutral delay difference equation where n โ Z, R, P, Q are nonnegative sequences and r, k, l are positive integers. New criteria, which do not need the conditions and/or for all sufficiently large n, are introduced. All the recent resu
Some oscillation criteria for difference equations
โ Scribed by Jianhua Shen; Zhiguo Luo
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 288 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0898-1221
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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 (\*\
First, we establish the equivalence of the oscillation of the delay difference equation โฌ x q p x s 0, Next, we obtain some sharp conditions for oscillations and nonoscillations of the first equation.
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.