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Oscillation of higher order neutral functional difference equations with positive and negative coefficients

In: Mathematica Slovaca, vol. 60, no. 3
R. N. Rath - B. L Barik - S. K Rath
Detaily:
Rok, strany: 2010, 361 - 384
Kľúčové slová:
oscillatory solution, nonoscillatory solution, asymptotic behaviour, difference equation
O článku:
Sufficient conditions are obtained so that every solution of the neutral functional difference equation

$$ Δm(yn-pnyτ(n)) + qnG(yσ(n))-unH(yα(n))=fn, $$

oscillates or tends to zero or $\pm ∞$ as $n\rightarrow∞$, where $Δ$ is the forward difference operator given by $Δ xn=xn+1-xn$, $pn$, $qn$, $un$, $fn$ are infinite sequences of real numbers with $qn>0$, $un ≥ 0$, $G, H \in C(\Bbb R ,\Bbb R )$ and $m ≥ 2$ is any positive integer. Various ranges of $\{pn\}$ are considered. The results hold for $G(u)\equiv u$, and $fn \equiv 0$. This paper corrects, improves and generalizes some recent results.
Ako citovať:
ISO 690:
Rath, R., Barik, B., Rath, S. 2010. Oscillation of higher order neutral functional difference equations with positive and negative coefficients. In Mathematica Slovaca, vol. 60, no.3, pp. 361-384. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0018-6

APA:
Rath, R., Barik, B., Rath, S. (2010). Oscillation of higher order neutral functional difference equations with positive and negative coefficients. Mathematica Slovaca, 60(3), 361-384. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0018-6
O vydaní: