Necessary and Sufficient Conditions for Oscillation of Nonlinear Second-Order Delay Differential Equations

References

[1] R. P. Agarwal, S. R. Grace, D. O'Regan, Oscillation Theory for Second Order Dynamic Equations, Taylor & Francis, London and New York, 2003.

[2] B. Baculikova, T. Li, J. Dzurina; Oscillation theorems for second order neutral differential equations, Elect. J. Quali. Theo. diff. equa., (74): (2011), 1-13.

[3] J. Dzurina; Oscillation theorems for second order advanced neutral differential equations, Tatra Mt. Math. Publ., DOI: 10.2478/v10127-011-0006-4, 48 (2011), 61-71.

[4] I. Gyori, G. Ladas; Oscillation Theory of Delay Differential Equations with Applications, Clarendon, Oxford, 1991.

[5] M. Hasanbulli, Y. V. Rogovchenko; Oscillation criteria forsecond order nonlinear neutral differential equations, Appl. Math. Comput., 215 (2010), 4392-4399.

[6] G. S. Ladde, V. Lakshmikantham, B. G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker, New York and Basel, 1987.

[7] T. Li, Yu. V. Rogovchenko, C. Zhang; Oscillation results for second-order nonlinear neutral differential equations, Adv. Di_erence Equ., 2013 (2013), 1-13.

[8] T. Li, Yu. V. Rogovchenko; Oscillation theorems for second-order nonlinear neutral delay differential equations, Abst. Appl. Anal, 2014 (2014), 1-5.

[9] Q. Li, R. Wang, F. Chen, T. Li; Oscillation of second-order nonlinear delay differential equations with nonpositive neutral coefficients, Adv. Diff. Eq. (2015) 2015:35. DOI 10.1186/s13662-015-0377-y.

[10] Y. Liu, J. Zhanga, J. Yan; Existence of oscillatory solutions of second order delay differential equations, J. Comp. Appl. Math., 277 (2015), 17-22.

[11] Q. Meng, J. Yan; Bounded oscillation for second order non-linear neutral delay differential equations in critical and non-critical cases, Nonlinear Anal., 64 (2006), 1543-1561.

[12] S. S. Santra; Existence of positive solution and new oscillation criteria for nonlinear first-order neutral delay differential equations, Diff. Equ. Appl., 8(1): (2016), 33-51.

[13] S. S. Santra, S. Pinelas; Qualitative behaviour for second order nonlinear delay differential equations of neutral type, Global J. Math., 8(3): (2016), 939-956.

[14] S. Tanaka; A oscillation theorem for a class of even order neutral differential equations, J. Math. Anal. Appl., 273 (2007), 172-189.

[15] R. Xu, F. Meng; Some new oscillation criteria for second order quasilinear neutral delay differential equations, Appl. Math. Comp., 182 (2006), 797-803.

[16] Z. Xu, P. Weng; Oscillation of second order neutral equations with distributed deviating argument, J. Comp. Appl. Math., 202 (2007), 460-477.

[17] J. Yan; Existence of oscillatory solutions of forced second order delay differential equations, Appl. Math. Lett. 24 (2011), 1455-1460.

[18] Q. Zhang, J. Yan; Oscillation behavior of even order neutral differential equations with variable coefficients, Appl. Math. Lett., 19 (2006), 1202-1206.