A Survey on Sharp Oscillation Conditions for Delay Difference Equations
PDF

Keywords

Oscillation
Several delays
Difference equations
Slowly varying sequence
Non-monotone argument

How to Cite

Benekas, V. ., & Kashkynbayev, A. . (2022). A Survey on Sharp Oscillation Conditions for Delay Difference Equations. Journal of Advances in Applied & Computational Mathematics, 8, 117–128. https://doi.org/10.15377/2409-5761.2021.08.9

Abstract

https://doi.org/10.15377/2409-5761.2021.08.9
PDF

References

Baštinec J, Berezansky L, Diblík J, Šmarda Z. A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation with a Positive Coefficient. Abstr Appl Anal 2011; Article ID 586328 (2011) https://doi.org/10.1155/2011/586328

Baštinec J, Diblík J, Šmarda Z. Oscillation of Solutions of a Linear Second-Order Discrete-Delayed Equation. Adv Differ Equ 2010; Article ID 693867 (2010) https://doi.org/10.1186/1687-1847-2010-693867

Braverman E, Karpuz B. On oscillation of differential and difference equations with non-monotone delays. Appl Math Comput 2011; 218: 3880-3887https://doi.org/10.1016/j.amc.2011.09.035

Chatzarakis GE, Stavroulakis IP. Oscillations of first order linear delay difference equations. Austral J Math Anal Appl 2006; 3(1): Art.14, 1-11.

Chen MP, Yu YS. Oscillations of delay difference equations with variable coefficients. Proc. First Intl. Conference on Difference Equations, (Edited by S.N. Elaydi et al), Gordon and Breach, 1995; 105-114.

Domshlak Y. Discrete version of Sturmian Comparison Theorem for non-symmetric equations. Dokl Azerb Acad Sci 1981; 37: 12-15 (in Russian).

Erbe LH, Zhang BG. Oscillation of discrete analogues of delay equations. Differential Integral Equations 1989; 2: 300-309.

Györi I, Ladas G. Oscillation Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford 1991.

Karpuz B. Sharp oscillation and nonoscillation tests for linear difference equations. J Difference Equ Appl 2017; 23(12): 1229-1242 https://doi.org/10.1080/10236198.2017.1379515

Ladas G. Recent developments in the oscillation of delay difference equations. In International Conference on Differential Equations, Stability and Control, Dekker, New York 1990.

Ladas G, Philos ChG, Sficas YG. Sharp conditions for the oscillation of delay difference equations. J Appl Math Simulation, 1989; 2: 101-112 https://doi.org/10.1155/S1048953389000080

Moremedi GM, Stavroulakis IP. Oscillation conditions for difference equations with a monotone or non-monotone argument. Discr Dyn Nat Soc 2018; Article ID 9416319 (2018) https://doi.org/10.1155/2018/9416319

Moremedi GM, Stavroulakis IP, Zhunussova ZK. Necessary and Sufficient Conditions for Oscillations of Functional Differential Equations. J Math Mech Comput Sci 2018; 99(3): 12-23 https://doi.org/10.26577/JMMCS-2018-3-528

Shen JH, Stavroulakis IP. Oscillation criteria for delay difference equations. Electron J. Diff Eqns 2001; 10: 1-15.

Stavroulakis IP. Oscillations of delay difference equations. Comput Math Applic 1995; 29: 83-88 https://doi.org/10.1016/0898-1221(95)00020-Y

Stavroulakis IP. Oscillation criteria for first order delay difference equations Mediterr J Math 2004; 1: 231-240 https://doi.org/10.1007/s00009-004-0013-7

Stavroulakis IP. A Survey on the Oscillation of Difference Equations with Constant Delays. J Math Mech Comput Sci 2019; 102(2): 3-11 https://doi.org/10.26577/JMMCS-2019-2-21

Tang XH, Deng YB. Oscillation of difference equations with several delays. Hunan Daxue Xuebao 1998; 25(2): 1-3.

Tang XH, Yu JS. Oscillation of delay difference equation. Comput Math Appl 1999; 37(7): 11-20. https://doi.org/10.1016/S0898-1221(99)00083-8

Tang XH, Zhang RY. New oscillation criteria for delay difference equations. Comput Math Applic 2001; 42(10-11): 1319-1330. https://doi.org/10.1016/S0898-1221(01)00243-7

Yu JS, Zhang BG, Wang ZC. Oscillation of delay difference equations. Appl Anal 1994; 53: 117-124 https://doi.org/10.1080/00036819408840248

Agarwal P. Difference Equations and Inequalities. Marcel Dekker, 1992.

Agarwal RP, Bohner M, Grace SR, O'Regan D. Discrete Oscillation Theory. Hindawi Publishing Corporation, New York 2005; https://doi.org/10.1155/9789775945198

Lakshmikantham V, Trigiante D. Theory of difference equations: Numerical methods and applications. Mathematics in Science and Engineering, 181, Academic Press, Boston, MA 1998.

Karpuz B, Stavroulakis IP. Oscillation and nonoscillation of difference equations with several delays. Mediterr J Math 2021; 18(1): Paper 15 pp. https://doi.org/10.1007/s00009-020-01617-0

Stavroulakis IP. Oscillations of delay and difference equations with variable coefficients and arguments, in: Differential and difference equations with applications, Springer Proc Math Stat 2016; 164: pp. 169-189. https://doi.org/10.1007/978-3-319-32857-7_17

Ladas G, Laskhmikantham V, Papadakis JS. Oscillations of higher-order retarded differential equations generated by retarded arguments. Delay and Functional Differential Equations and Their Applications, Academic Press, New York 1972; 219-231. https://doi.org/10.1016/B978-0-12-627250-5.50013-7

Koplatadze RG, Chanturija TA. On the oscillatory and monotonic solutions of first order differential equations with deviating arguments, Differentsial'nye Uravneniya 1982; 18: 1463-1465.

Garab Á, Pituk M, Stavroulakis IP. A sharp oscillation criterion for a linear delay differential equation. Appl Math Letters 2019; 93: 58-65 https://doi.org/10.1016/j.aml.2019.01.042

Ash JM, Erdös P, Rubel LA. Very slowly varying functions, Aequat. Math. 1974; 10: 1-9. https://doi.org/10.1007/BF01834775

Seneta E. Regularly varying functions, Lecture Notes in Mathematics, 1976; 508, Springer-Verlag, Berlin-New York, https://doi.org/10.1007/BFb0079658

Pituk M. Oscillation of a linear delay differential equation with slowly varying coefficient. Appl Math Letters 2017; 73: 29-36. https://doi.org/10.1016/j.aml.2017.04.019

Garab Á. A sharp oscillation criterion for a linear differential equation with variable delay. Symmetry. 2019; 11(11): Article ID 1332. https://doi.org/10.3390/sym11111332

Garab Á, Stavroulakis IP. Oscillation criteria for first order linear delay differential equations with several variable delays. Appl Math Lett 2020; 106: Article ID 106366 https://doi.org/10.1016/j.aml.2020.106366

Benekas V, Kashkynbayev A, Stavroulakis IP. A sharp oscillation criterion for a difference equation with constant delay. Adv Differ Equ 2020; 566 (2020). https://doi.org/10.1186/s13662-020-03016-x

Chatzarakis GE, Pinelas S, Stavroulakis IP. Correction to: Oscillations of difference equations with several deviated arguments. Aequationes Math 2018; 92: 1195-1200. https://doi.org/10.1007/s00010-018-0581-4

Chatzarakis GE, Pinelas S, Stavroulakis IP. Oscillations of difference equations with several deviated arguments. Aequationes Math 2014; 88: 105-123. https://doi.org/10.1007/s00010-013-0238-2

Benekas V, Garab Á, Kashkynbayev A, Stavroulakis IP. Oscillation criteria for linear difference equations with several variable delays. Opuscula Math 2021; 41(5): 613-627 (2021). https://doi.org/10.7494/OpMath.2021.41.5.613

Yan W, Meng Q, Yan JR. Oscillation criteria for difference equation of variable delays. Dyn Contin Discret Impuls Syst Ser A Math Anal 2006; 13A(Part 2): 641-647.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2021 Vasileios Benekas, Ardak Kashkynbayev