Oscillation tests for nonlinear differential equations with nonmonotone delays

In this paper, our aim is to investigate a class of first-order nonlinear delay differential equations with severaldeviating arguments. In addition, we present some sufficient conditions for the oscillatory solutions of these equations.Differing from other studies in the literature, delay terms are not necessarily monotone. Finally, we give examples todemonstrate the results.

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[1] Agarwal RP, Bohner M, Li T, Zhang C. A new approach in the study of oscillatory behavior of evenorder neutral delay differential equations. Applied Mathematics and Computation 2013; 225: 787-794. doi: 10.1016/j.amc.2013.09.037
[2] Bohner M, Li T. Oscillation of second-order p-Laplace dynamic equations with a nonpositive neutral coefficient. Applied Mathematics Letters 2014; 37: 72-76. doi: 10.1016/j.aml.2014.05.012
[3] Braverman E, Karpuz B. On oscillation of differential and difference equations with nonmonotone delays. Applied Mathematics and Computation 2011; 218 (7): 3880-3887. doi: 10.1016/j.amc.2011.09.035
4] Bravermen E, Chatzarakis GE, Stavroulakis IP. Iterative oscillation tests for differential equations with several non-monotone arguments. Advances in Difference Equations 2016; 2016 (1): 1-18. doi: 10.1186/s13662-016-0817-3
[5] Chatzarakis GE, Li T. Oscillations of differential equations generated by several deviating arguments. Advances in Difference Equations 2017; 2017 (1): 1-24. doi: 10.1186/s13662-017-1353-5
[6] Chatzarakis GE, Jadlovská I. Improved iterative oscillation tests for first-order deviating differential equations. Opuscula Mathematica 2018; 38 (3): 327-356. doi: 10.7494/OpMath.2018.38.3.327
[7] Chatzarakis GE, Li T. Oscillation criteria for delay and advanced differential equations with nonmonotone arguments. Complexity 2018; 2018. doi: 10.1155/2018/8237634
[8] Chatzarakis GE. Oscillations of equations caused by several deviating arguments. Opuscula Mathematica 2019; 39 (3): 321-353. doi: 10.7494/OpMath.2019.39.3.321
[9] Chatzarakis GE, Jadlovská I. Oscillations in deviating differential equations using an iterative method. Communications in Mathematics 2019; 27 (2): 143-169. doi: 10.2478/cm-2019-0012
[10] Chatzarakis GE, Jadlovská I. Explicit criteria for the oscillation of differential equations with several arguments. Dynamic Systems and Applications 2019; 28 (2): 217-242. doi: 10.12732/dsa.v28i2.1
[11] Chatzarakis GE, Jadlovská I, Li T. Oscillations of differential equations with nonmonotone deviating arguments. Advances in Difference Equations 2019; 2019 (1): 1-20. doi: 10.1186/s13662-019-2162-9
[12] Chatzarakis GE. Oscillation test for linear deviating differential equations. Applied Mathematics Letters 2019; 98: 352-358. doi: 10.1016/j.aml.2019.06.022
[13] Chatzarakis GE, Grace SR, Jadlovská I, Li T, Tunç E. Oscillation criteria for third-order Emden-Fowler differential equations with unbounded neutral coefficients. Complexity 2019; 2019: 1-7, Article ID 5691758. doi: 10.1155/2019/5691758
[14] Chatzarakis GE, Jadlovská I. Oscillations in differential equations caused by non-monotone arguments. Nonlinear Studies 2020; 27 (3): 589-607.
[15] Chatzarakis GE. Oscillation of deviating differential equations. Mathematica Bohemica 2020; 145 (4): 435-448. doi: 10.21136/MB.2020.0002-19
[16] Dix JP, Dix JG. Oscillation of solutions to nonlinear first-order delay differential equations. Involve 2016; 9 (3): 465-482. doi: 10.2140/involve.2016.9.465
[17] Džurina J, Grace SR, Jadlovská I, Li T. Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term. Mathematische Nachrichten 2020; 293 (5): 910-922. doi: 10.1002/mana.201800196
[18] Erbe LH, Kong Q, Zhang BG. Oscillation Theory for Functional Differential Equations. New York, NY, USA: Marcel Dekker, 1995.
[19] Fukagai N, Kusano T. Oscillation theory of first order functional differential equations with deviating arguments. Annali di Matematica Pura ed Applicata 1984; 136 (1): 95-117. doi: 10.1007/BF01773379
[20] Győri I, Ladas G. Oscillation Theory of Delay Differential Equations with Applications. Oxford, UK: Clarendon Press, 1991.
[21] Koplatadze RG, Chanturija TA. Oscillating and monotone solutions of first-order differential equations with deviating arguments (Russian). Differentsial’nye Uravneniya 1982; 18 (8): 1463-1465.
[22] Ladde GS, Lakshmikantham V, Zhang BG. Oscillation Theory of Differential Equations with Deviating Arguments. Monographs and Textbooks in Pure and Applied Mathematics 110. New York, NY, USA: Marcel Dekker, 1987.
[23] Li T, Rogovchenko YV. Oscillation criteria for even-order neutral differential equations. Applied Mathematics Letters 2016; 61: 35-41. doi: 10.1016/j.aml.2016.04.012
[24] Li T, Rogovchenko YV. On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Applied Mathematics Letters 2020; 105: 1-7, Article ID 106293. doi: 10.1016/j.aml.2020.106293
[25] Öcalan Ö, Kılıç N, Şahin S, Özkan UM. Oscillation of nonlinear delay differential equation with nonmonotone arguments. International Journal of Analysis and Applications 2017; 14 (2): 147-154.
[26] Öcalan Ö, Kılıç N, Özkan UM, Öztürk S. Oscillatory behavior for nonlinear delay differential equation with several non-monotone arguments. Computational Methods for Differential Equations 2020; 8 (1): 14-27. doi: 10.22034/cmde.2019.9470