| Title:
|
An improved oscillation theorem for nonlinear differential equations of advanced type (English) |
| Author:
|
Kiliç, Nurten |
| Author:
|
Öcalan, Özkan |
| Author:
|
Yildiz, Mustafa Kemal |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2024 |
| Pages:
|
145-152 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with the oscillatory solutions of the first order nonlinear advanced differential equation. The aim of the present paper is to obtain an oscillation condition for this equation. This result is new and improves and correlates many of the well-known oscillation criteria that were in the literature. Finally, an example is given to illustrate the main result. (English) |
| Keyword:
|
advanced equations |
| Keyword:
|
nonmonotone argument |
| Keyword:
|
oscillatory solution |
| MSC:
|
34C10 |
| MSC:
|
34K06 |
| MSC:
|
34K11 |
| DOI:
|
10.5817/AM2024-3-145 |
| . |
| Date available:
|
2024-08-02T08:34:05Z |
| Last updated:
|
2024-08-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152522 |
| . |
| Reference:
|
[1] Kılıç, N., Öcalan, Ö., Özkan, U.M.: Oscillation tests for nonlinear differential equations with several nonmonotone advanced arguments.Appl. Math. E-Notes 21 (2021), 253–262. MR 4269225 |
| Reference:
|
[2] Koplatadze, R.G., Chanturija, T.A.: Oscillating and monotone solutions of first-order differential equations with deviating arguments.Differ. Uravn. 8 (1982), 1463–1465. MR 0671174 |
| Reference:
|
[3] Kulenovic, M.R., Grammatikopoulos, M.K.: Some comparison and oscillation results for first order differential equations and inequalities with a deviating argument.J. Math. Anal. Appl. 131 (1988), 67–84. MR 0934431, 10.1016/0022-247X(88)90190-4 |
| Reference:
|
[4] Kusano, T.: On even order functional differential equations with advanced and retarded arguments.J. Differential Equations 45 (1982), 75–84. MR 0662487, 10.1016/0022-0396(82)90055-9 |
| Reference:
|
[5] Ladas, G., Stavroulakis, I.P.: Oscillations caused by several retarded and advanced arguments.J. Differential Equations 44 (1982), 134–152. MR 0651691, 10.1016/0022-0396(82)90029-8 |
| Reference:
|
[6] Ladde, G.S., Lakshmikantham, V., Zhang, B.G.: Oscillation Theory of Differential Equations with Deviating Arguments.Monographs and Textbooks in Pure and Applied Mathematics, vol. 110, Marcel Dekker, Inc., New York, 1987. Zbl 0832.34071, MR 1017244 |
| Reference:
|
[7] Li, X., Zhu, D.: Oscillation and nonoscillation of advanced differential equations with variable coefficients.J. Math. Anal. Appl. 269 (2002), 462–488. MR 1907126, 10.1016/S0022-247X(02)00029-X |
| Reference:
|
[8] Öcalan, Ö., Kılıç, N., Özkan, U.M.: Oscillatory behavior of nonlinear advanced differential equations with a non-monotone argument.Acta Math. Univ. Comenian. (N.S.) 88 (2019), 239–246. MR 3984642 |
| Reference:
|
[9] Öcalan, Ö., Özkan, U.M.: Oscillations of dynamic equations on time scales with advanced arguments.Int. J. Dyn. Syst. Differ. Equ. 6 (2016), 275–284. MR 3607086 |
| . |
