We establish the oscillatory solutions of a second order half-linear neutral delay difference equations of the form
for nn0 > 0, N(n0) = { n0, n0 + 1, … } n0 is a non negative integer and α is ratio of odd positive integers. Where
for all nN(n0), with the condition
By using the classical Riccati transformation techniques, we present new oscillation criteria of studied equations and examples are provided to illustrate the main results.
1.
Agarwal
,
R.P.
,
Wong
,
P.J.Y.
:
Advanced Topics in Difference Equations
,
Kluwer Academic Publishers
,
Drodrecht
.
1997
.
2.
R. P.
Agarwal
,
S. R.
Grace
,
D.
ORegan
,
Oscillation Theory for Difference and Functional Differential Equations
,
Kluwer Academic
,
Dordrecht
,
2000
.
3.
T.
Asaela
,
H.
YoshidaH
,
Stability, instability and complex behavior in macrodynamic models with policy lag
,
Discrete Dynamics in Nature and Society
,
5
, (
2001
),
281
295
.
4.
Andruch-Sobilo
,
A.
,
Migda
,
M.
:
On the oscillation of solutions of third order linear difference equations of neutral type
.
Math. Bohem.
130
,
19
33
(
2005
).
5.
Artzroumi
,
M.
:
Generalized stable population theory
.
J. Math. Biology.
21
,
363
381
(
1985
).
6.
B.
Baculkova
,
J.
Dzurina
,
Oscillation of third order neutral differential equations
,
Math. Comput. Modelling
,
52
, (
2010
),
215
226
.
7.
L.
Berenzansky
,
E.
Braverman
,
Some oscillation problems for a second order linear delay differential equations
,
J. Math. Anal. Appl.
220
, (
1998
),
719
740
.
8.
C.
Cesarano
and
O.
Bazighifan
,
Qualitative behavior of solutions of second order differential equations
,
Symmetry (MDPI)
,
11
(
777
) (
2019
)
8
pages.
9.
Dosla
,
Z.
,
Kobza
,
A.
:
Global asymptotic properties of third-order difference equations
.
Comput. Math. Appl.
48
,
191
200
(
2004
).
10.
Dosla
,
Z.
,
Kobza
,
A.
:
On third-order linear difference equations involving quasi-differences
.
Adv. Difference Equ.
1
13
(
2006
).
11.
O.
Dosly
,
J.
Graef
,
J.
Jaros
,
Forced oscillation of second order linear and half linear difference equations
,
Proc. Amer. Math. Soc.
131
(
2002
),
2859
2867
.
This content is only available via PDF.
You do not currently have access to this content.