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Li, Tongxing; Han, Zhenlai; Zhao, Ping; Sun, Shurong

Oscillation of even-order neutral delay differential equations. (English) Zbl 1209.34082

Adv. Difference Equ. 2010, Article ID 184180, 9 p. (2010).
By employing the Riccati transformation technique, the authors establish some new oscillation criteria for even order neutral delay differential equations. An illustrative example is given.
Reviewer: Qiru Wang (Guangzhou)

Cited in 25 Documents

MSC:

34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations

Keywords:

neutral delay differential equations; even order; Riccati transformation technique
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\textit{T. Li} et al., Adv. Difference Equ. 2010, Article ID 184180, 9 p. (2010; Zbl 1209.34082)
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References:

[1] Hale J: Theory of Functional Differential Equations, Applied Mathematical Sciences, vol. 3. 2nd edition. Springer, New York, NY, USA; 1977:x+365.
[2] Džurina J, Stavroulakis IP: Oscillation criteria for second-order delay differential equations.Applied Mathematics and Computation 2003,140(2-3):445-453. 10.1016/S0096-3003(02)00243-6 · Zbl 1043.34071
[3] Grace SR: Oscillation theorems for nonlinear differential equations of second order.Journal of Mathematical Analysis and Applications 1992,171(1):220-241. 10.1016/0022-247X(92)90386-R · Zbl 0767.34017
[4] Koplatadze R: On oscillatory properties of solutions of functional differential equations.Memoirs on Differential Equations and Mathematical Physics 1994, 3: 1-180.
[5] Philos ChG: A new criterion for the oscillatory and asymptotic behavior of delay differential equations.Bulletin de l’Académie Polonaise des Science, Série des Sciences Mathématiques 1981, 39: 61-64.
[6] Sun YG, Meng FW: Note on the paper of J. Džurina and I. P. Stavroulakis.Applied Mathematics and Computation 2006,174(2):1634-1641. 10.1016/j.amc.2005.07.008 · Zbl 1096.34048
[7] Agarwal RP, Grace SR: Oscillation theorems for certain neutral functional-differential equations.Computers & Mathematics with Applications 1999,38(11-12):1-11. 10.1016/S0898-1221(99)00280-1 · Zbl 0981.34059
[8] Han Z, Li T, Sun S, Sun Y: Remarks on the paper [Appl. Math. Comput. 207 (2009) 388-396].Applied Mathematics and Computation 2010,215(11):3998-4007. 10.1016/j.amc.2009.12.006 · Zbl 1188.34086
[9] Han, Z.; Li, T.; Sun, S.; Chen, W., On the oscillation of second order neutral delay differential equations, No. 2010, 8 (2010) · Zbl 1192.34074
[10] Grammatikopoulos MK, Ladas G, Meimaridou A: Oscillations of second order neutral delay differential equations.Radovi Matematički 1985,1(2):267-274. · Zbl 0581.34051
[11] Karpuz B, Manojlović JV, Öcalan Ö, Shoukaku Y: Oscillation criteria for a class of second-order neutral delay differential equations.Applied Mathematics and Computation 2009,210(2):303-312. 10.1016/j.amc.2008.12.075 · Zbl 1188.34087
[12] Lin X, Tang XH: Oscillation of solutions of neutral differential equations with a superlinear neutral term.Applied Mathematics Letters 2007,20(9):1016-1022. 10.1016/j.aml.2006.11.006 · Zbl 1152.34364
[13] Liu L, Bai Y: New oscillation criteria for second-order nonlinear neutral delay differential equations.Journal of Computational and Applied Mathematics 2009,231(2):657-663. 10.1016/j.cam.2009.04.009 · Zbl 1175.34087
[14] Meng F, Xu R: Oscillation criteria for certain even order quasi-linear neutral differential equations with deviating arguments.Applied Mathematics and Computation 2007,190(1):458-464. 10.1016/j.amc.2007.01.040 · Zbl 1131.34319
[15] Rath RN, Misra N, Padhy LN: Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation.Mathematica Slovaca 2007,57(2):157-170. 10.2478/s12175-007-0006-7 · Zbl 1150.34026
[16] Şahiner Y: On oscillation of second order neutral type delay differential equations.Applied Mathematics and Computation 2004,150(3):697-706. 10.1016/S0096-3003(03)00300-X · Zbl 1045.34038
[17] Xu R, Xia Y: A note on the oscillation of second-order nonlinear neutral functional differential equations.International Journal of Contemporary Mathematical Sciences 2008,3(29-32):1441-1450. · Zbl 1176.34078
[18] Xu R, Meng F: New Kamenev-type oscillation criteria for second order neutral nonlinear differential equations.Applied Mathematics and Computation 2007,188(2):1364-1370. 10.1016/j.amc.2006.11.004 · Zbl 1142.34360
[19] Xu R, Meng F: Oscillation criteria for second order quasi-linear neutral delay differential equations.Applied Mathematics and Computation 2007,192(1):216-222. 10.1016/j.amc.2007.01.108 · Zbl 1193.34137
[20] Xu Z, Liu X: Philos-type oscillation criteria for Emden-Fowler neutral delay differential equations.Journal of Computational and Applied Mathematics 2007,206(2):1116-1126. 10.1016/j.cam.2006.09.012 · Zbl 1122.34045
[21] Ye L, Xu Z: Oscillation criteria for second order quasilinear neutral delay differential equations.Applied Mathematics and Computation 2009,207(2):388-396. 10.1016/j.amc.2008.10.051 · Zbl 1168.34346
[22] Zafer A: Oscillation criteria for even order neutral differential equations.Applied Mathematics Letters 1998,11(3):21-25. 10.1016/S0893-9659(98)00028-7 · Zbl 0933.34075
[23] Zhang Q, Yan J, Gao L: Oscillation behavior of even-order nonlinear neutral differential equations with variable coefficients.Computers and Mathematics with Applications 2010,59(1):426-430. 10.1016/j.camwa.2009.06.027 · Zbl 1189.34135
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