Araştırma Makalesi
Yıl 2025,
Erken Görünüm, 1 - 1
Öz
Kaynakça
- [1] Agarwal, R. P., Wong, Y. J., “Advanced Topics in Difference Equations”, Kluwer, Dordrecht, (1997).
- [2] Agarwal, R. P., “Difference Equations and Inequalities, Theory, Methods and Applications”, Second Edition, Marcel Dekker, New York, (2000).
- [3] Elaydi, S., “An Introduction to Difference Equations”, Third Edition, Springer, New York, (2005).
- [4] Gyori, I., Ladas, G., “Oscillation Theory of Delay Differential Equations with Applications”, Clarendon, Oxford, (1991).
- [5] Parhi, N., “Oscillation and non-oscillation of solutions of second order difference equations involving generalized difference”, Applied Mathematics and Computation, 218: 458-468, (2011). DOI: 10.1016/j.amc.2011.05.086
- [6] Bolat, Y., Akın, Ö., “Oscillation criteria for higher-order half-linear delay difference equations involving generalized difference”, Math. Slovaca, 66(3): 677-686, (2016). DOI: 10.1515/ms-2015-0169
- [7] Bezubik, A., Migda, M., Nockowska-Rosiak, M., Schmeidel, E., “Trichotomy of nonoscillatory solutions to second-order neutral difference equation with quasi-difference”, Advances in Difference Equations, 2015: 192, (2015). DOI: 10.1186/s13662-015-0531-6
- [8] Cheng, S. S., Patula, W. T., “An existence theorem for a nonlinear difference equation”, Non- linear Anal. 20: 193-203, (1993).
- [9] Saker, S. H., “Oscillation Criteria of Second-order Half-linear Delay Difference Equations”, Kyungpook Math. J., 45: 579-594, (2005).
- [10] Saker, S. H., “Oscillation of Second-order Nonlinear Difference Equations”, Bull Korean Math. Soc. 40(3): 489-501, (2003). DOI: 10.4134/BKMS.2003.40.3.489
- [11] Vidhyaa, K., Thandapani, E., Alzabut, J., Özbekler, A., “Oscillation Criteria for Non-Canonical Second Order Nonlinear Delay Difference Equations with a Superlinear Neutral Term”, Electronic Journal of Differential Equations, 2023(45): 1-12, (2023). DOI: 10.58997/ejde.2023.45
- [12] Tan, M., Yang, E., “Oscillation and nonoscillation theorems for second order nonlinear difference equations”, J. Math. Anal. Appl., 276: 239-247, (2002). DOI: 10.1016/S0022-247X(02)00435-3
- [13] Zhang, Z., Bi, P., Chen, J., “Oscillation of Second Order Nonlinear Difference Equation with Continuous Variable”, Journal of Mathematical Analysis and Applications, 255: 349–357, (2001).
Trichotomy of nonoscillatory solutions for nonlinear first- order neutral difference equation with generalized difference operators
Öz
In this study, we examine the trichotomy of non-oscillatory solution for the nonlinear first-order neutral difference equation
∆_a (x_n-a^(n+1) x_(n-1) )+∆_a (x_(n-1)/b_(n-1) )+q_n f(x_(n-τ) )=0,n∈N_max{1,τ} ,
where ∆_a x_n=x_(n+1)-ax_n,τ∈N,a∈R^+ with ∆_a^m Δ=∆_a^(m-1) (∆_a ), aⁿ is a general term of exponential sequence, (q_n) is real valued sequences. The accuracy of the primary findings is demonstrated by examples.
Anahtar Kelimeler
Trichotomy Oscillation Nonoscillation Neutral difference equation Generalized difference operators.
Kaynakça
- [1] Agarwal, R. P., Wong, Y. J., “Advanced Topics in Difference Equations”, Kluwer, Dordrecht, (1997).
- [2] Agarwal, R. P., “Difference Equations and Inequalities, Theory, Methods and Applications”, Second Edition, Marcel Dekker, New York, (2000).
- [3] Elaydi, S., “An Introduction to Difference Equations”, Third Edition, Springer, New York, (2005).
- [4] Gyori, I., Ladas, G., “Oscillation Theory of Delay Differential Equations with Applications”, Clarendon, Oxford, (1991).
- [5] Parhi, N., “Oscillation and non-oscillation of solutions of second order difference equations involving generalized difference”, Applied Mathematics and Computation, 218: 458-468, (2011). DOI: 10.1016/j.amc.2011.05.086
- [6] Bolat, Y., Akın, Ö., “Oscillation criteria for higher-order half-linear delay difference equations involving generalized difference”, Math. Slovaca, 66(3): 677-686, (2016). DOI: 10.1515/ms-2015-0169
- [7] Bezubik, A., Migda, M., Nockowska-Rosiak, M., Schmeidel, E., “Trichotomy of nonoscillatory solutions to second-order neutral difference equation with quasi-difference”, Advances in Difference Equations, 2015: 192, (2015). DOI: 10.1186/s13662-015-0531-6
- [8] Cheng, S. S., Patula, W. T., “An existence theorem for a nonlinear difference equation”, Non- linear Anal. 20: 193-203, (1993).
- [9] Saker, S. H., “Oscillation Criteria of Second-order Half-linear Delay Difference Equations”, Kyungpook Math. J., 45: 579-594, (2005).
- [10] Saker, S. H., “Oscillation of Second-order Nonlinear Difference Equations”, Bull Korean Math. Soc. 40(3): 489-501, (2003). DOI: 10.4134/BKMS.2003.40.3.489
- [11] Vidhyaa, K., Thandapani, E., Alzabut, J., Özbekler, A., “Oscillation Criteria for Non-Canonical Second Order Nonlinear Delay Difference Equations with a Superlinear Neutral Term”, Electronic Journal of Differential Equations, 2023(45): 1-12, (2023). DOI: 10.58997/ejde.2023.45
- [12] Tan, M., Yang, E., “Oscillation and nonoscillation theorems for second order nonlinear difference equations”, J. Math. Anal. Appl., 276: 239-247, (2002). DOI: 10.1016/S0022-247X(02)00435-3
- [13] Zhang, Z., Bi, P., Chen, J., “Oscillation of Second Order Nonlinear Difference Equation with Continuous Variable”, Journal of Mathematical Analysis and Applications, 255: 349–357, (2001).
Toplam 13 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Adi Diferansiyel Denklemler, Fark Denklemleri ve Dinamik Sistemler |
| Bölüm | Research Article |
| Yazarlar | |
| Erken Görünüm Tarihi | 8 Mart 2025 |
| Yayımlanma Tarihi | |
| Gönderilme Tarihi | 30 Ekim 2023 |
| Kabul Tarihi | 14 Aralık 2024 |
| Yayımlandığı Sayı | Yıl 2025 Erken Görünüm |