We establish the oscillatory solutions of a second order half-linear neutral delay difference equations of the form for n ≥ n0 > 0, N(n0) = { n0, n0 + 1, … } n0 is a non negative integer and α is ratio of odd positive integers. Where for all n ∈ N(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.
Topics
Recurrence relations
REFERENCES
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
.
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