Oscillation conditions for difference equations with several variable arguments

Title:

Oscillation conditions for difference equations with several variable arguments

Creator:

Chatzarakis, George E., Kusano, Takaŝi, and Stavroulakis, Ioannis P.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:0c80b2e1-1c77-46cf-a435-6465576c3f96
uuid:0c80b2e1-1c77-46cf-a435-6465576c3f96
doi:10.21136/MB.2015.144396

Subject:

difference equation, retarded argument, advanced argument, oscillatory solution, and nonoscillatory solution

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Consider the difference equation ∆x(n) +∑m i=1 pi(n)x(τi(n)) = 0, n ≥ 0 [ ∇x(n) − ∑m i=1 pi(n)x(σi(n)) = 0, n ≥ 1 ] , where (pi(n)), 1 6 i 6 m are sequences of nonnegative real numbers, τi(n) [σi(n)], 1 6 i 6 m are general retarded (advanced) arguments and ∆ [∇] denotes the forward (backward) difference operator ∆x(n) = x(n + 1) − x(n) [∇x(n) = x(n) − x(n − 1)]. New oscillation criteria are established when the well-known oscillation conditions lim sup n→∞ ∑m i=1 ∑n j=τ(n) pi(j) > 1 [ lim sup n→∞ ∑m i=1 σ∑ (n) j=n pi(j) > 1 ] and lim inf n→∞ ∑m i=1 n∑−1 j=τi(n) pi(j) > 1⁄e [ lim inf n→∞ ∑m i=1 σ∑i(n) j=n+1 pi(j) > 1⁄e ] are not satisfied. Here τ (n) = max 1≤i≤m τi(n) [σ(n) = min 1≤i≤m σi(n)]. The results obtained essentially improve known results in the literature. Examples illustrating the results are also given.

Language:

English

Rights:

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

Coverage:

291-311

Source:

Mathematica bohemica | 2015 Volume:140 | Number:3

Harvested from:

CDK

Metadata only:

false