Oscillatory behavior of second-order nonlinear noncanonical neutral differential equations

[1] R. P. Agarwal, M. Bohner, T. Li, and C. Zhang, Oscillation of second-order differential equations with a sublinear neutral term, Carpathian J. Math., 30 (2014), 1–6. Search in Google Scholar

[2] R. P. Agarwal, C. Zhang, and T. Li, Some remarks on oscillation of second order neutral differential equations, Appl. Math. Comput., 274 (2016), 178–181. Search in Google Scholar

[3] M. Bohner, S. R. Grace, and I. Jadlovská, Oscillation criteria for second-order neutral delay differential equations, Electron. J. Qual. Theory Diff. Equ., 2017 (2017), No. 60, 1–12. Search in Google Scholar

[4] M. Bohner, B. Sudha, K. Tangavelu, and E. Thandapani, Oscillation criteria for second-order differential equations with superlinear neutral term, Nonlinear Stud., 26 (2019), 425–434. Search in Google Scholar

[5] M. Bohner, S. R. Grace and I. Jadlovská, Sharp oscillation criteria for second-order neutral delay differential equations, Math. Meth. Appl. Sci., 43 (2020), 10041–10053. Search in Google Scholar

[6] R. K. Brayton, and R. A. Willoughby, On the numerical integration of a symmetric system of difference-differential equations of neutral type, J. Math. Anal. Appl., 18 (1967), 182–189. Search in Google Scholar

[7] J. G. Dong, Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments, Comput. Math. Appl., 59 (2010), 3710–3717. Search in Google Scholar

[8] S. R. Grace, J. D˘zurina, I. Jadlovská and T. Li, An improved approach for studying oscillation of second-order neutral delay differential equations, J. Inequalities Appl., 2018 (2018), 1–13. Search in Google Scholar

[9] S. R. Grace and J. R. Graef, Oscillatory behavior of second order nonlinear differential equations with a sublinear neutral term, Math. Model. Anal., 23 (2018), 217–226. Search in Google Scholar

[10] S. R. Grace, J. R. Graef, T. Li and E. Tunç, Oscillatory behavior of second-order nonlinear differential equations with mixed neutral terms, Tatra Mt. Math. Publ., 79 (2021), 119–134. Search in Google Scholar

[11] S. R. Grace, J. R. Graef and E. Tunç, Oscillation of second-order nonlinear noncanonical dynamic equations with deviating arguments, Acta Math. Univ. Comenianae, 91 (2022), 113–120. Search in Google Scholar

[12] J. R. Graef, M. K. Grammatikopoulos, and P. W. Spikes, Asymptotic behavior of nonoscillatory solutions of neutral delay differential equations of arbitrary order, Nonlinear Anal., 21 (1993), 23–42. Search in Google Scholar

[13] J. R. Graef, M. K. Grammatikopoulos, and P. W. Spikes, On the asymptotic behavior of solutions of a second order nonlinear neutral delay differential equation, J. Math. Anal. Appl., 156 (1991), 23–39. Search in Google Scholar

[14] J. R. Graef and P. W. Spikes, Some asymptotic properties of solutions of a neutral delay equation with an oscillatory coefficient, Canadian Math. Bull., 36 (1993), 263–272. Search in Google Scholar

[15] J. R. Graef and P. W. Spikes, Asymptotic and oscillatory behavior of solutions of nonlinear neutral delay equations of arbitrary order, Appl. Math. Comput., 65 (1994), 209–221. Search in Google Scholar

[16] J. K. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977. Search in Google Scholar

[17] I. Jadlovská, New criteria for sharp oscillation of second-order neutral delay differential equations, Mathematics, 9 (2021), 1–23. Search in Google Scholar

[18] T. Li, Y. V. Rogovchenko, and C. Zhang, Oscillation of second-order neutral differential equations, Funkcial. Ekvac., 56 (2013), 111–120. Search in Google Scholar

[19] T. Li, E. Thandapani, J. R. Graef and E. Tunç, Oscillation of second-order Emden-Fowler neutral differential equations, Nonlinear Stud., 20 (2013), 1–8. Search in Google Scholar

[20] T. Li and Y. V. Rogovchenko, Oscillation of second-order neutral differential equations, Math. Nachr., 288 (2015), 1150–1162. Search in Google Scholar

[21] T. Li and Y. V. Rogovchenko, Oscillation criteria for second-order super-linear Emden–Fowler neutral differential equations, Monatsh. Math., 184 (2017), 489–500. Search in Google Scholar

[22] N. Prabaharan, C. P. Dharuman, J. R. Graef, and E. Thandapani, New oscillation criteria for second order quasi-linear differential equations with sub-linear neutral term, Appl. Math. E-Notes, 19 (2019), 563–574. Search in Google Scholar

[23] S. H. Saker, R. P. Agarwal, and D. O’Regan, Oscillation results for second-order nonlinear neutral delay dynamic equations on time scales, Appl. Anal., 86 (2007), 1–17. Search in Google Scholar

[24] A. K. Sethi and A. K. Tripathy, On oscillatory second-order differential equations with variable delays, Palestine J. Math., 10 (2021), 487–501. Search in Google Scholar

[25] M. Slemrod and E. F. Infante, Asymptotic stability criteria for linear systems of difference-differential equations of neutral type and their discrete analogues, J. Math. Anal. Appl., 38 (1972), 399–415. Search in Google Scholar

[26] Y. Sui and Z. Han, Oscillation of second order neutral dynamic equations with deviating arguments on time scales, Adv. Differ. Equ., 2018 (2018), 1–10. Search in Google Scholar

[27] S. Tamilvanan, E. Thandapani, and J. D˘zurina, Oscillation of second order nonlinear differential equation with sub-linear neutral term, Differ. Equ. Appl., 9 (2017), 29–35. Search in Google Scholar

[28] A. K. Tripathy and S. S. Santra, Necessary and sufficient conditions for oscillation of second-order differential equations with nonpositive neutral coefficients, Math. Bohem., 146 (2021), 185–197. Search in Google Scholar

[29] R. Xu and F. Meng, Some new oscillation criteria for second order quasi-linear neutral delay differential equations, Appl. Math. Comput., 182 (2006), 797–803. Search in Google Scholar