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Open Access Research Article

Sufficient conditions for the oscillation of solutions of third-order neutral difference equations with alternating coefficients

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pp. 1085–1090Vol. 29Issue 5-AMay 2026DOI: 10.47974/JIM-2287XML
Received:
01 May 2025
Published Online:
27 Jun 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2287
Pages:
1085–1090

Abstract

This study deals with 3rd-order difference equations with alternating coefficients (NDEAC) with a focus on studying the oscillatory properties of their solutions. An additional sufficient condition can be derived to ensure continuity for the oscillatory solution in equations. An applied example is presented to illustrate the theoretical result obtained.

Keywords

Subject Classifications

39A1039A13

References

[1] A. Murugesan and K. Shanmugavalli, “Oscillation conditions for first-order neutral difference equations with positive and negative variable coefficients,” Malaya Journal of Matematik, vol. 5, no. 2, pp. 378–388 (2017).
[2] H. A. El-Morshedy, “New oscillation criteria for second-order linear difference equations with positive and negative coefficients,” Computers & Mathematics with Applications, vol. 58, no. 10, pp. 1988–1997 (2009), doi: 10.1016/j.camwa.2009.07.078. 
[3] S. H. Saker, “Oscillation of second-order nonlinear neutral delay dynamic equations on time scales,” Journal of Computational and Applied Mathematics, vol. 187, no. 2, pp. 123–141 (2006).
[4] X. Liu, D. Deng, and H. Wang, “Oscillation of a nonlinear neutral difference equation with positive and negative coefficients,” Journal of Applied Analysis and Computation, vol. 3, no. 2, Art. no. 32003 (2018), doi: 10.22606/jaam.2018.32003.
[5] A. Jawad and A. F. Jaddoa, “On the existence and oscillatory solutions of multiple delay differential equation,” Iraqi Journal of Science, vol. 64, no. 2, pp. 878–892 (2023), doi: 10.24996/ijs.2023.64.2.33.
[6] I. Z. Mushtt, D. M. Hameed, and B. M. Alwan, “On oscillating outcomes for non-homogenous neutral difference equations of a third order,” Journal of Interdisciplinary Mathematics, vol. 24, no. 5, pp. 1387–1395 (2021).
[7] S. N. Ketab and S. F. Raji, “Oscillation and nonoscillation criteria for second-order half-linear neutral difference equations,” Journal of Interdisciplinary Mathematics, vol. 25, no. 5, pp. 1525–1533 (2022), doi: 10.1080/09720502.2022.2087295.
[8] H. A. Mohamad and S. N. Ketab, “Asymptotic behavior criteria for solutions of nonlinear n-th order neutral differential equations,” IOP Conference Series: Materials Science and Engineering, vol. 571, no. 1, Art. no. 012034 (2019), doi: 10.1088/1757-899X/571/1/012034. 
[9] I. Z. Mushtt, H. M. Mohi, and I. H. Qasem, “Nonoscillatory properties for solution of nonlinear neutral difference equations of second order with positive and negative coefficients,” IJCET, vol. 10, no. 1, pp. 462–468 (2019).    
[10] I. Győri and G. E. Ladas, Oscillation Theory of Delay Differential Equations: With Applications. New York, USA: Oxford University Press (Clarendon Press), pp. 368 (1991). 
[11] M. K. Yildiz, B. Karpuz, and Ö. Öcalan, “Oscillation of nonlinear neutral delay differential equations of second order with positive and negative coefficients,” Turkish Journal of Mathematics, vol. 33, no. 4, pp. 341–350 (2009).

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