ABSTRACT
This paper is concerned with the oscillation criteria of odd-order non-linear differential equations with mixed non-linear neutral terms. We provide new oscillation criteria that improve, expand, and simplify existing ones. Moreover, some examples are provided to demonstrate the theoretical findings.
Acknowledgement
We would like to thank all the reviewers for their valuable comments and suggestions which helped us to improve the manuscript.
REFERENCES
[1] Agarwal, R. P.—Grace, S. R.—O’Regan, D.: Oscillation Theory for Second Order Linear, Half-linear, Superlinear and Sublinear Dynamic Equations, Springer, 2002.10.1007/978-94-017-2515-6Search in Google Scholar
[2] Agarwal, R. P.—Bohner, M.—Li, T.—Zhang, C.: A new approach in the study of oscillatory behavior of even-order neutral delay differential equations, Appl. Math. Comput. 225 (2013), 787–794.10.1016/j.amc.2013.09.037Search in Google Scholar
[3] Agarwal, R. P.—Grace, S. R.: Oscillation theorems for certain functional differential equations of higher order, Math. Comput. Model. 39(9–10) (2004), 1185–1194.10.1016/S0895-7177(04)90539-0Search in Google Scholar
[4] Agarwal, R. P.—Grace, S. R.—O’Regan, D.: Oscillation criteria for certain nth order differential equations with deviating arguments, J. Math. Anal. Appl. 262(2) (2001), 601–622.10.1006/jmaa.2001.7571Search in Google Scholar
[5] Agarwal, R. P.—Grace, S. R.—O’Regan, D.: Oscillation Theory for Difference and Functional Differential Equations, Springer, 2013.Search in Google Scholar
[6] Bainov, D. D.—Mishev, D. P.: Oscillation Theory for Neutral Differential Equations with Delay, CRC Press, 1991.Search in Google Scholar
[7] Bohner, M.—Li, T.: Oscillation of second-order p-Laplace dynamic equations with a nonpositive neutral coefficient, Appl. Math. Lett. 37 (2014), 72–76.10.1016/j.aml.2014.05.012Search in Google Scholar
[8] Chiu, K. S.—Li, T.: Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments, Math. Nachr. 292(10) (2019), 2153–2164.10.1002/mana.201800053Search in Google Scholar
[9] Džurina, J.—Kotorová, R.: Properties of the third order trinomial differential equations with delay argument, Nonlinear Anal. 71(5–6) (2009), 1995–2002.10.1016/j.na.2009.01.070Search in Google Scholar
[10] Džurina, J.—Grace, S. R.—Jadlovská, I.—Li, T.: Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr. 293(5) (2020), 910–922.10.1002/mana.201800196Search in Google Scholar
[11] Erbe, L. H.—Kong, Q.—Zhang, B. G.: Oscillation Theory for Functional Differential Equations, Marcel Dekker Inc., New York, 1995.Search in Google Scholar
[12] Grace, S. R.—Agarwal, R. P.—Bohner, M.—Oregan, D.: Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations, Commun. Nonlinear Sci. Numer. Simul. 14(8) (2009), 3463–3471.10.1016/j.cnsns.2009.01.003Search in Google Scholar
[13] Grace, S. R.—Agarwal, R. P.—Kaymakalan, B.—Sae-Jie, W.: Oscillation theorems for second order nonlinear dynamic equations, Appl. Math. Comput. 32 (2010), 205–218.10.1007/s12190-009-0244-7Search in Google Scholar
[14] Grace, S. R.—Akin, E.—Dikmen, C. M.: On the oscillation of second order nonlinear neutral dynamic equations with distributed deviating arguments on time scales, Dynam. Systems Appl. 23 (2014), 735–748.Search in Google Scholar
[15] Grace, S. R.—Graef, J. R.—El-Beltagy, M. A.: On the oscillation of third order neutral delay dynamic equations on time scales, Comput. Math. Appl. 63 (2012), 775–782.10.1016/j.camwa.2011.11.042Search in Google Scholar
[16] Grace, S. R.—Chhatria, G. N.—Abbas, S.: Oscillation properties of solutions of second order neutral dynamic equations of non-canonical type on time scales, Qual. Theory Dyn. Syst. 21 (2022), Art. No 17.10.1007/s12346-021-00552-zSearch in Google Scholar
[17] Grace, S. R.—Bohner, M.—Agarwal, R. P.: On the oscillation of second order half-linear dynamic equations, J. Difference Equ. Appl. 15 (2009), 451–460.10.1080/10236190802125371Search in Google Scholar
[18] Grace, S. R.—Negi, S. S.—Abbas, S.: New oscillatory results for non-linear delay dynamic equations with super-linear neutral term, Appl. Math. Comput. 412 (2022), Art. ID 126576.10.1016/j.amc.2021.126576Search in Google Scholar
[19] Graef, J. R.—Saker, S. H.: Oscillation theory of third-order nonlinear functional differential equations, Hiroshima Math. J. 43(1) (2013), 49–72.10.32917/hmj/1368217950Search in Google Scholar
[20] Hale, J. K.—Lunel, S. M. V.: Introduction to Functional Differential Equations, Springer, New York, 1993.10.1007/978-1-4612-4342-7Search in Google Scholar
[21] Hardy, G. H.—Littlewood, J. E.—Pólya, G.—Pólya, G.: Inequalities, Cambridge University Press, 1952.Search in Google Scholar
[22] Kiguradze, I. T.: On the oscillation of solutions of equation
[23] Koplatadze, R. G.—Chanturiya, T. A. E.: Oscillating and monotone solutions of first-order differential equations with deviating argument, Differentsial’nye Uravneniya 18(8) (1982), 1463–1465.Search in Google Scholar
[24] Li, T.—Rogovchenko, Y. V.—Zhang, C.: Oscillation results for second-order nonlinear neutral differential equations, Adv. Difference Equ. 2013 (2013), Art. No. 336.10.1186/1687-1847-2013-336Search in Google Scholar
[25] Li, T.—Rogovchenko, Y. V.: Oscillation criteria for second-order superlinear Emden-Fowler neutral differential equations, Monatsh. Math. 184(3) (2017), 489–500.10.1007/s00605-017-1039-9Search in Google Scholar
[26] Li, T.—Rogovchenko, Y. V.: Oscillation criteria for even-order neutral differential equations, Appl. Math. Lett. 61 (2016), 35–41.10.1016/j.aml.2016.04.012Search in Google Scholar
[27] Negi, S. S.—Abbas, S.—Malik, M.: Oscillation for a nonlinear neutral dynamic equations on timescales with variable exponents, Math. Methods Appl. Sci. 42(12) (2019), 4146–4169.10.1002/mma.5636Search in Google Scholar
[28] Negi, S. S.—Abbas, S.—Malik, M.—Grace, S. R.: New oscillation criteria for p-Laplacian dynamic equations on time scales, Rocky Mountain J. Math. 50(2) (2020), 659–670.10.1216/rmj.2020.50.659Search in Google Scholar
[29] Qin, H.—Shang, N.—Lu, Y.: A note on oscillation criteria of second order nonlinear neutral delay differential equations, Comput. Math. Appl. 56(12) (2008), 2987–2992.10.1016/j.camwa.2008.09.004Search in Google Scholar
[30] Wong, J. S. W.: Necessary and sufficient conditions for oscillation of second order neutral differential equations, J. Math. Anal. Appl. 252 (2000), 342–353.10.1006/jmaa.2000.7063Search in Google Scholar
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