Author:
Manuel Mariasebastin Maria Susai,Kılıçman Adem,Srinivasan K,Babu G Dominic
Abstract
Abstract
In this paper, the authors discuss the oscillation of solutions of some generalized nonlinear α-difference equation
Δ
α
(
ℓ
)
(
p
(
k
)
Δ
α
(
ℓ
)
u
(
k
)
)
+
q
(
k
)
f
(
u
(
k
−
τ
(
k
)
)
)
=
0
,
k
∈
[
a
,
∞
)
, where the functions p, q, f and τ are defined in their domain of definition and
α
>
1
, ℓ is a positive real. Further,
u
f
(
u
)
>
0
for
u
≠
0
,
p
(
k
)
>
0
and
lim
k
→
∞
(
k
−
τ
(
k
)
)
=
∞
, where
R
k
=
∑
r
=
0
[
k
−
ℓ
ℓ
]
1
α
r
p
(
r
ℓ
)
→
∞
as
k
→
∞
and
u
(
k
)
is defined for
k
≥
min
i
≥
0
(
i
−
τ
(
i
)
)
for all
k
∈
[
a
,
∞
)
for some
a
∈
[
0
,
∞
)
.
MSC:39A12.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference13 articles.
1. Agarwal RP: Difference Equations and Inequalities. Dekker, New York; 2000.
2. Mickens RE: Difference Equations. Reinhold, New York; 1990.
3. Elaydi SN: An Introduction to Difference Equations. 2nd edition. Springer, Berlin; 1999.
4. Kelley WG, Peterson AC: Difference Equations. An Introduction with Applications. Academic Press, New York; 1991.
5. Manuel MMS, Kılıçman A, Xavier GBA, Pugalarasu R, Dilip DS:"Equation missing" No EquationSource Format="TEX", only image and EquationSource Format="MATHML" and "Equation missing" No EquationSource Format="TEX", only image and EquationSource Format="MATHML" solutions of a second order generalized difference equation. Adv. Differ. Equ. 2012., 2012: Article ID 105
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