Title:
|
Oscillations of nonlinear difference equations with deviating arguments (English) |
Author:
|
Chatzarakis, George E. |
Author:
|
Dix, Julio G. |
Language:
|
English |
Journal:
|
Mathematica Bohemica |
ISSN:
|
0862-7959 (print) |
ISSN:
|
2464-7136 (online) |
Volume:
|
143 |
Issue:
|
1 |
Year:
|
2018 |
Pages:
|
67-87 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
This paper is concerned with the oscillatory behavior of first-order nonlinear difference equations with variable deviating arguments. The corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given. (English) |
Keyword:
|
infinite sum condition |
Keyword:
|
retarded argument |
Keyword:
|
advanced argument |
Keyword:
|
oscillatory solution |
Keyword:
|
nonoscillatory solution |
MSC:
|
39A10 |
MSC:
|
39A21 |
idZBL:
|
Zbl 06861592 |
idMR:
|
MR3778050 |
DOI:
|
10.21136/MB.2017.0055-16 |
. |
Date available:
|
2018-03-19T10:34:43Z |
Last updated:
|
2020-07-01 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147142 |
. |
Reference:
|
[1] Berezansky, L., Braverman, E.: On existence of positive solutions for linear difference equations with several delays.Adv. Dyn. Syst. Appl. 1 (2006), 29-47. Zbl 1124.39002, MR 2287633 |
Reference:
|
[2] Chatzarakis, G. E., Koplatadze, R., Stavroulakis, I. P.: Optimal oscillation criteria for first order difference equations with delay argument.Pac. J. Math. 235 (2008), 15-33. Zbl 1153.39010, MR 2379767, 10.2140/pjm.2008.235.15 |
Reference:
|
[3] Chatzarakis, G. E., Pinelas, S., Stavroulakis, I. P.: Oscillations of difference equations with several deviated arguments.Aequationes Math. 88 (2014), 105-123. Zbl 1306.39007, MR 3250787, 10.1007/s00010-013-0238-2 |
Reference:
|
[4] Chatzarakis, G. E., Stavroulakis, I. P.: Oscillations of first order linear delay difference equations.Aust. J. Math. Anal. Appl. (electronic only) 3 (2006), Article ID 14, 11 pages. Zbl 1096.39003, MR 2223018 |
Reference:
|
[5] Dix, J. P., Dix, J. G.: Oscillations of solutions to nonlinear first-order delay differential equations.Involve 9 (2016), 465-482. Zbl 06590119, MR 3509339, 10.2140/involve.2016.9.465 |
Reference:
|
[6] Erbe, L. H., Kong, Q., Zhang, B. G.: Oscillation Theory for Functional-Differential Equations.Pure and Applied Mathematics 190. Marcel Dekker, New York (1994). Zbl 0821.34067, MR 1309905 |
Reference:
|
[7] Erbe, L. H., Zhang, B. G.: Oscillation of discrete analogues of delay equations.Differ. Integral Equ. 2 (1989), 300-309. Zbl 0723.39004, MR 0983682 |
Reference:
|
[8] Ladas, G.: Explicit conditions for the oscillation of difference equations.J. Math. Anal. Appl. 153 (1990), 276-287. Zbl 0718.39002, MR 1080131, 10.1016/0022-247X(90)90278-N |
Reference:
|
[9] Ladas, G., Philos, C. G., Sficas, Y. G.: Sharp conditions for the oscillation of delay difference equations.J. Appl. Math. Simulation 2 (1989), 101-111. Zbl 0685.39004, MR 1010549, 10.1155/S1048953389000080 |
Reference:
|
[10] Ladde, G. S., Lakshmikantham, V., Zhang, B. G.: Oscillation Theory of Differential Equations with Deviating Arguments.Pure and Applied Mathematics 110. Marcel Dekker, New York (1987). Zbl 0622.34071, MR 1017244 |
Reference:
|
[11] Li, B.: Oscillation of first order delay differential equations.Proc. Am. Math. Soc. 124 (1996), 3729-3737. Zbl 0865.34057, MR 1363175, 10.1090/S0002-9939-96-03674-X |
Reference:
|
[12] Li, X., Zhu, D.: Oscillation of advanced difference equations with variable coefficients.Ann. Differ. Equations 18 (2002), 254-263. Zbl 1010.39001, MR 1940383 |
Reference:
|
[13] Luo, X. N., Zhou, Y., Li, C. F.: Oscillation of a nonlinear difference equation with several delays.Math. Bohem. 128 (2003), 309-317. Zbl 1055.39015, MR 2012607 |
Reference:
|
[14] Tang, X. H., Yu, J. S.: Oscillation of delay difference equation.Comput. Math. Appl. 37 (1999), 11-20. Zbl 0937.39012, MR 1688201, 10.1016/S0898-1221(99)00083-8 |
Reference:
|
[15] Tang, X. H., Zhang, R. Y.: New oscillation criteria for delay difference equations.Comput. Math. Appl. 42 (2001), 1319-1330. Zbl 1002.39022, MR 1861531, 10.1016/S0898-1221(01)00243-7 |
Reference:
|
[16] Wang, X.: Oscillation of delay difference equations with several delays.J. Math. Anal. Appl. 286 (2003), 664-674. Zbl 1033.39017, MR 2008855, 10.1016/S0022-247X(03)00508-0 |
Reference:
|
[17] Yan, W., Meng, Q., Yan, J.: Oscillation criteria for difference equation of variable delays.Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 13A (2006), Part 2, suppl., 641-647. MR 2219618 |
Reference:
|
[18] Zhang, B. G., Zhou, Y.: Oscillations of difference equations with several delays.Comput. Math. Appl. 44 (2002), 817-821. Zbl 1035.39010, MR 1925823, 10.1016/S0898-1221(02)00193-1 |
. |