Asymptotic behaviour of solutions of third order nonlinear difference equations of neutral type

Title:

Asymptotic behaviour of solutions of third order nonlinear difference equations of neutral type

Creator:

Andruch-Sobiło, Anna and Drozdowicz, Andrzej

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:00796923-17a8-4c83-a1a8-91ffe7e64f3a
uuid:00796923-17a8-4c83-a1a8-91ffe7e64f3a
doi:10.21136/MB.2008.140615

Subject:

neutral type difference equation, third order difference equation, nonoscillatory solutions, and asymptotic behavior

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In the paper we consider the difference equation of neutral type (E) ∆3 [x(n) − p(n)x(σ(n))] + q(n)f(x(τ (n))) = 0, n ∈ N(n0 ), where p, q : N(n0 ) → R+; σ, τ : N → Z, σ is strictly increasing and lim n→∞ σ(n) = ∞; τ is nondecreasing and lim n→∞ τ (n) = ∞, f : R → R, xf(x) > 0. We examine the following two cases: 0 < p(n) ≤ λ ∗ < 1, σ(n) = n − k, τ (n) = n − l, and 1 < λ∗ ≤ p(n), σ(n) = n + k, τ (n) = n + l, where k, l are positive integers. We obtain sufficient conditions under which all nonoscillatory solutions of the above equation tend to zero as n → ∞ with a weaker assumption on q than the usual assumption ∑∞ i=n0 q(i) = ∞ that is used in literature.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

247-258

Source:

Mathematica bohemica | 2008 Volume:133 | Number:3

Harvested from:

CDK

Metadata only:

false