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Qualitative properties of solutions of higher order difference equations with deviating arguments
Monotonic solutions of a higher-order neutral difference system
1. | Institute of Mathematics, University of Białystok, Ciolkowskiego 1M, 15-245 Bialystok, Poland |
2. | Institute of Mathematics, Lodz University of Technology, Wolczanska 215, 90-924 Lodz, Poland |
A class of a higher-order nonlinear difference system with delayed arguments where the first equation of the system is of a neutral type is considered. A classification of non-oscillatory solutions is given and results on their boundedness or unboundedness are derived. The obtained results are illustrated by examples.
References:
[1] |
R. P. Agarwal, S. R. Grace and E. Akin-Bohner,
On the oscillation of higher order neutral difference equations of mixed type, Dynam. Systems Appl., 11 (2002), 459-469.
|
[2] |
R. P. Agarwal, E. Thandapani and P. J. Y. Wong,
Oscillations of higher order neutral difference equations, Appl. Math. Lett., 10 (1997), 71-78.
doi: 10.1016/S0893-9659(96)00114-0. |
[3] |
Y. Bolat,
Oscillation of higher order neutral type nonlinear difference equations with forcing terms, Chaos, Solitons, Fractals, 42 (2009), 2973-2980.
doi: 10.1016/j.chaos.2009.04.006. |
[4] |
J. Diblík, B. Łupińska, M. Růžičková and J. Zonenberg,
Boundedness and unboundedness of non-oscillatory solutions of a four-dimensional nonlinear neutral difference system, Boundedness and unboundedness of non-oscillatory solutions of a four-dimensional nonlinear neutral difference system, 2015 (2015), 1-11.
doi: 10.1186/s13662-015-0662-9. |
[5] |
J. R. Graef, A. Miciano, P. Spikes, P. Sundaram and E. Thandapani,
Oscilatory and asymptotic behavior of solutions of nonlinear neutral-type difference equations, J. Austral. Math. Soc. Ser. B, 38 (1996), 163-171.
doi: 10.1017/S0334270000000552. |
[6] |
R. Jankowski and E. Schmeidel,
Asymptotically zero solution of a class of higher nonlinear neutral difference equations with quasidifferences, Discrete Contin. Dyn. Syst. (B), 19 (2014), 2691-2696.
doi: 10.3934/dcdsb.2014.19.2691. |
[7] |
R. Jankowski, E. Schmeidel and J. Zonenberg,
Oscillatory properties of solutions of the fourth order difference equations with quasidifferences, Opuscula Math., 34 (2014), 789-797.
doi: 10.7494/OpMath.2014.34.4.789. |
[8] |
W. T. Li and S. S. Cheng,
Asymptotic trichotomy for positive solutions of a class of odd order nonlinear neutral difference equations, Comput. Math. Appl., 35 (1998), 101-108.
doi: 10.1016/S0898-1221(98)00048-0. |
[9] |
M. Migda,
On unstable neutral difference equations of higher order, Indian J. Pure Appl. Math., 36 (2005), 557-567.
|
[10] |
M. Migda and J. Migda,
Asymptotic properties of solutions of second-order neutral difference equations, Nonlinear Anal., 63 (2005), e789-e799.
doi: 10.1016/j.na.2005.02.005. |
[11] |
M. Migda and J. Migda,
Oscillatory and asymptotic properties of solutions of even order neutral difference equations, J. Difference Equ. Appl., 15 (2009), 1077-1084.
doi: 10.1080/10236190903032708. |
[12] |
N. Parhi and A. K. Tripathy,
Oscillation of a class of nonlinear neutral difference equations of higher order, J. Math. Anal. Appl., 284 (2003), 756-774.
doi: 10.1016/S0022-247X(03)00298-1. |
[13] |
E. Schmeidel,
Asymptotic trichotomy of solutions of a class of even order nonlinear neutral difference equations with quasidifferences, Proceedings of the International Conference on Difference Equations, Special Functions and Orthogonal Polynomials, World Scientific Publishing Co, (2007), 600-609.
doi: 10.1142/9789812770752_0052. |
[14] |
A. Zafer,
Oscillatory and asymptotic behavior of higher order difference equations, Math. Comput. Modelling, 21 (1995), 43-50.
doi: 10.1016/0895-7177(95)00005-M. |
[15] |
Y. Zhou and B. G. Zhang,
Existence of nonoscillatory solutions of higher-order neutral delay difference equations with variable coefficients, Comput. Math. Appl., 45 (2003), 991-1000.
doi: 10.1016/S0898-1221(03)00074-9. |
show all references
References:
[1] |
R. P. Agarwal, S. R. Grace and E. Akin-Bohner,
On the oscillation of higher order neutral difference equations of mixed type, Dynam. Systems Appl., 11 (2002), 459-469.
|
[2] |
R. P. Agarwal, E. Thandapani and P. J. Y. Wong,
Oscillations of higher order neutral difference equations, Appl. Math. Lett., 10 (1997), 71-78.
doi: 10.1016/S0893-9659(96)00114-0. |
[3] |
Y. Bolat,
Oscillation of higher order neutral type nonlinear difference equations with forcing terms, Chaos, Solitons, Fractals, 42 (2009), 2973-2980.
doi: 10.1016/j.chaos.2009.04.006. |
[4] |
J. Diblík, B. Łupińska, M. Růžičková and J. Zonenberg,
Boundedness and unboundedness of non-oscillatory solutions of a four-dimensional nonlinear neutral difference system, Boundedness and unboundedness of non-oscillatory solutions of a four-dimensional nonlinear neutral difference system, 2015 (2015), 1-11.
doi: 10.1186/s13662-015-0662-9. |
[5] |
J. R. Graef, A. Miciano, P. Spikes, P. Sundaram and E. Thandapani,
Oscilatory and asymptotic behavior of solutions of nonlinear neutral-type difference equations, J. Austral. Math. Soc. Ser. B, 38 (1996), 163-171.
doi: 10.1017/S0334270000000552. |
[6] |
R. Jankowski and E. Schmeidel,
Asymptotically zero solution of a class of higher nonlinear neutral difference equations with quasidifferences, Discrete Contin. Dyn. Syst. (B), 19 (2014), 2691-2696.
doi: 10.3934/dcdsb.2014.19.2691. |
[7] |
R. Jankowski, E. Schmeidel and J. Zonenberg,
Oscillatory properties of solutions of the fourth order difference equations with quasidifferences, Opuscula Math., 34 (2014), 789-797.
doi: 10.7494/OpMath.2014.34.4.789. |
[8] |
W. T. Li and S. S. Cheng,
Asymptotic trichotomy for positive solutions of a class of odd order nonlinear neutral difference equations, Comput. Math. Appl., 35 (1998), 101-108.
doi: 10.1016/S0898-1221(98)00048-0. |
[9] |
M. Migda,
On unstable neutral difference equations of higher order, Indian J. Pure Appl. Math., 36 (2005), 557-567.
|
[10] |
M. Migda and J. Migda,
Asymptotic properties of solutions of second-order neutral difference equations, Nonlinear Anal., 63 (2005), e789-e799.
doi: 10.1016/j.na.2005.02.005. |
[11] |
M. Migda and J. Migda,
Oscillatory and asymptotic properties of solutions of even order neutral difference equations, J. Difference Equ. Appl., 15 (2009), 1077-1084.
doi: 10.1080/10236190903032708. |
[12] |
N. Parhi and A. K. Tripathy,
Oscillation of a class of nonlinear neutral difference equations of higher order, J. Math. Anal. Appl., 284 (2003), 756-774.
doi: 10.1016/S0022-247X(03)00298-1. |
[13] |
E. Schmeidel,
Asymptotic trichotomy of solutions of a class of even order nonlinear neutral difference equations with quasidifferences, Proceedings of the International Conference on Difference Equations, Special Functions and Orthogonal Polynomials, World Scientific Publishing Co, (2007), 600-609.
doi: 10.1142/9789812770752_0052. |
[14] |
A. Zafer,
Oscillatory and asymptotic behavior of higher order difference equations, Math. Comput. Modelling, 21 (1995), 43-50.
doi: 10.1016/0895-7177(95)00005-M. |
[15] |
Y. Zhou and B. G. Zhang,
Existence of nonoscillatory solutions of higher-order neutral delay difference equations with variable coefficients, Comput. Math. Appl., 45 (2003), 991-1000.
doi: 10.1016/S0898-1221(03)00074-9. |
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