Author:
Gao Yali,Sun Yuangong,Zha Bin,Liu Hongshuang
Abstract
Abstract
In this paper, we study the forced oscillation of the higher-order nonlinear difference equation of the form
Δ
m
[
x
(
n
)
−
p
(
n
)
x
(
n
−
τ
)
]
+
q
1
(
n
)
Φ
α
(
n
−
σ
1
)
+
q
2
(
n
)
Φ
β
(
n
−
σ
2
)
=
f
(
n
)
,
where
m
≥
1
, τ,
σ
1
and
σ
2
are integers,
0
<
α
<
1
<
β
are constants,
Φ
∗
(
u
)
=
|
u
|
∗
−
1
u
,
p
(
n
)
,
q
1
(
n
)
,
q
2
(
n
)
and
f
(
n
)
are real sequences with
p
(
n
)
>
0
. By taking all possible values of τ,
σ
1
and
σ
2
into consideration, we establish some new oscillation criteria for the above equation in two cases: (i)
q
1
=
q
1
(
n
)
≤
0
,
q
2
=
q
2
(
n
)
>
0
; (ii)
q
1
≥
0
,
q
2
<
0
.
MSC:39A10.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference22 articles.
1. Agarwal RP: Difference Equations and Inequalities: Theory, Methods, and Applications. Dekker, New York; 1992.
2. Agarwal RP, Wong PJY: Advanced Topics in Difference Equations. Kluwer Academic, Dordrecht; 1997.
3. Györi I, Ladas G: Oscillation Theory of Delay Differential Equations. Clarendon, Oxford; 1991.
4. Sun YG, Saker SH: Oscillation for second-order nonlinear neutral delay difference equations. Appl. Math. Comput. 2005, 163: 909–918. 10.1016/j.amc.2004.04.017
5. Agarwal RP, Manuel MMS, Thandapani E: Oscillatory and nonoscillatory behavior of second-order neutral delay difference equations. Math. Comput. Model. 1996, 24: 5–11. 10.1016/0895-7177(96)00076-3
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献