In the paper the general higher order difference equation
$(-1)^z Δ^m x(n)=f(n, x(σ_1(n)),x(σ_2(n)),..., x(σ_k(n)))$
with several deviating arguments is considered. According to the kind of the deviations $σ_i$ sufficient conditions for the equation to have property A and B are established.
Citation: |
R. P. Agarwal, M. Bohner, S. R. Grace and D. O'Regan,
Discrete Oscillation Theory Hindawi Publishing Corporation, New York, 2005.
doi: 10.1155/9789775945198.![]() ![]() ![]() |
|
R. P. Agarwal,
Difference Equations and Inequalities. Theory, Methods, and Applications Second Edition, Revised and Expanded, Marcel Dekker, New York, 2000.
![]() ![]() |
|
J. Baštinec, L. Berezansky, J. Diblík and Z. šmarda, A final result on the oscillation of solutions of the linear discrete delayed equation $Δ x(n)=-p(n)x(n-k)$ with a positive coefficient Abstract and Applied Analysis 2011 (2011), Art. ID 586328, 28 pp.
doi: 10.1155/2011/586328.![]() ![]() ![]() |
|
G. E. Chatzarakis
, R. Koplatadze
and I. P. Stavroulakis
, Oscillation criteria of first order linear difference equations with delay argument, Nonlinear Anal., 68 (2008)
, 994-1005.
doi: 10.1016/j.na.2006.11.055.![]() ![]() ![]() |
|
G. E. Chatzarakis
, M. Lafci
and I. P. Stavroulakis
, Oscillation results for difference equations with several oscillating coefficients, Applied Mathematics and Computation, 251 (2015)
, 81-91.
doi: 10.1016/j.amc.2014.11.045.![]() ![]() ![]() |
|
G. E. Chatzarakis
, Ch. G. Philos
and I. P. Stavroulakis
, On the oscillation of the solutions to linear difference equations with variable delay, Electron. J. Differ. Equ., 50 (2008)
, 1-15.
![]() ![]() |
|
G. E. Chatzarakis
and Ö. Öcalan
, Oscillation of difference equations with non-monotone retarded arguments, Applied Mathematics and Computation, 258 (2015)
, 60-66.
doi: 10.1016/j.amc.2015.01.110.![]() ![]() ![]() |
|
G. E. Chatzarakis, H. Péics, S. Pinelas and I. P. Stavroulakis, Oscillation results for difference equations with oscillating coefficients Advances in Difference Equations 2015 (2015), 17pp.
doi: 10.1186/s13662-015-0391-0.![]() ![]() ![]() |
|
L. H. Erbe
and B. G. Zhang
, Oscillation of discrete analogues of delay equations, Differential Integral Equations, 2 (1989)
, 300-309.
![]() ![]() |
|
G. Grzegorczyk
and J. Werbowski
, On oscillatory solutions of certain difference equations, Opuscula Mathematica, 26 (2006)
, 317-326.
![]() ![]() |
|
G. Grzegorczyk
and J. Werbowski
, Oscillation of higher-order linear difference equations, Comput. Math. Appl., 42 (2001)
, 711-717.
doi: 10.1016/S0898-1221(01)00190-0.![]() ![]() ![]() |
|
I. Györi and G. Ladas,
Oscillation Theory of Delay Differential Equations with Applications Clarendon Press, Oxford, New York, 1991.
![]() ![]() |
|
W. G. Kelley and A. C. Peterson,
Difference Equations. An Introduction with Applications Second edition, Harcourt/Academic Press, San Diego, CA, 2001.
![]() ![]() |
|
G. Ladas
, Ch. G. Philos
and Y. G. Sficas
, Sharp conditions for the oscillation of delay difference equations, J. Appl. Math. Simulation, 2 (1989)
, 101-111.
doi: 10.1155/S1048953389000080.![]() ![]() ![]() |
|
J. Migda, Approximative solutions of difference equations,
Electron. J. Qual. Theory Differ. Equ. 13 (2014), 26 pp.
![]() ![]() |
|
M. Migda
, Existence of nonoscillatory solutions of some higher order difference equations, Appl. Math. E-Notes, 4 (2004)
, 33-39.
![]() ![]() |
|
M. Migda
and J. Migda
, On the asymptotic behavior of solutions of higher order nonlinear difference equations, Nonlinear Analysis, 47 (2001)
, 4687-4695.
doi: 10.1016/S0362-546X(01)00581-8.![]() ![]() ![]() |
|
M. Migda
, Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations, Opuscula Mathematica, 26 (2006)
, 507-514.
![]() ![]() |
|
W. Nowakowska
and J. Werbowski
, On connections between oscillatory solutions of functional, difference and differential equations, Fasc. Math., 44 (2010)
, 95-106.
![]() ![]() |
|
Ch. G. Philos
, I. K. Purnaras
and I. P. Stavroulakis
, Sufficient conditions for the oscillation of delay difference equations, J. Difference Equ. Appl., 10 (2004)
, 419-435.
doi: 10.1080/10236190410001648239.![]() ![]() ![]() |
|
J. Werbowski
, Bounded oscillations of differential equations generated by deviating arguments, Utilitas Math., 31 (1987)
, 191-198.
![]() ![]() |
|
A. Wyrwińska
, Oscillation criteria of a higher order linear difference equation, Bull. Inst. Math. Acad. Sinica, 22 (1994)
, 259-266.
![]() ![]() |