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Tian, Yazhou; Cai, Yuanli; Fu, Youliang; Li, Tongxing

Oscillation and asymptotic behavior of third-order neutral differential equations with distributed deviating arguments. (English) Zbl 1422.34196

Adv. Difference Equ. 2015, Paper No. 267, 14 p. (2015).
Summary: By employing a generalized Riccati transformation and integral averaging technique, two Philos-type criteria are obtained which ensure that every solution of a class of third-order neutral differential equations with distributed deviating arguments is either oscillatory or converges to zero. These results extend and improve related criteria reported in the literature. Two illustrative examples are provided.

Cited in 20 Documents

MSC:

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

Keywords:

oscillation; asymptotic behavior; third-order neutral differential equation; distributed deviating argument; generalized Riccati transformation
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References:

[1] Wang, PG: Oscillation criteria for second-order neutral equations with distributed deviating arguments. Comput. Math. Appl. 47, 1935-1946 (2004) · Zbl 1070.34086 · doi:10.1016/j.camwa.2002.10.016
[2] Agarwal, RP, Grace, SR, O’Regan, D: Oscillation Theory for Difference and Functional Differential Equations. Kluwer Academic, Dordrecht (2000) · Zbl 0954.34002 · doi:10.1007/978-94-015-9401-1
[3] Agarwal, RP, Grace, SR, O’Regan, D: Oscillation Theory for Second Order Dynamic Equations. Taylor & Francis, London (2003) · Zbl 1043.34032 · doi:10.4324/9780203222898
[4] Aktaş, MF, Tiryaki, A, Zafer, A: Oscillation criteria for third-order nonlinear functional differential equations. Appl. Math. Lett. 23, 756-762 (2010) · Zbl 1194.34127 · doi:10.1016/j.aml.2010.03.003
[5] Baculíková, B, Džurina, J: Oscillation of third-order neutral differential equations. Math. Comput. Model. 52, 215-226 (2010) · Zbl 1201.34097 · doi:10.1016/j.mcm.2010.02.011
[6] Baculíková, B, Džurina, J: Oscillation of third-order functional differential equations. Electron. J. Qual. Theory Differ. Equ. 2010, 43 (2010) · Zbl 1211.34077
[7] Candan, T: Asymptotic properties of solutions of third-order nonlinear neutral dynamic equations. Adv. Differ. Equ. 2014, 35 (2014) · Zbl 1351.34107 · doi:10.1186/1687-1847-2014-35
[8] Candan, T: Oscillation criteria and asymptotic properties of solutions of third-order nonlinear neutral differential equations. Math. Methods Appl. Sci. 38, 1379-1392 (2015) · Zbl 1322.34089 · doi:10.1002/mma.3153
[9] Grace, SR, Agarwal, RP, Pavani, R, Thandapani, E: On the oscillation of certain third order nonlinear functional differential equations. Appl. Math. Comput. 202, 102-112 (2008) · Zbl 1154.34368 · doi:10.1016/j.amc.2008.01.025
[10] Jiang, Y, Li, T: Asymptotic behavior of a third-order nonlinear neutral delay differential equation. J. Inequal. Appl. 2014, 512 (2014) · Zbl 1372.34115 · doi:10.1186/1029-242X-2014-512
[11] Li, HJ: Oscillation criteria for second order linear differential equations. J. Math. Anal. Appl. 194, 217-234 (1995) · Zbl 0836.34033 · doi:10.1006/jmaa.1995.1295
[12] Li, T, Rogovchenko, YuV, Zhang, C: Oscillation results for second-order nonlinear neutral differential equations. Adv. Differ. Equ. 2013, 336 (2013) · Zbl 1391.34112 · doi:10.1186/1687-1847-2013-336
[13] Li, T, Saker, SH: A note on oscillation criteria for second-order neutral dynamic equations on isolated time scales. Commun. Nonlinear Sci. Numer. Simul. 19, 4185-4188 (2014) · Zbl 1470.34239 · doi:10.1016/j.cnsns.2014.04.015
[14] Li, T, Zhang, C, Xing, G: Oscillation of third-order neutral delay differential equations. Abstr. Appl. Anal. 2012, Article ID 569201 (2012). doi:10.1155/2012/569201 · Zbl 1232.34097 · doi:10.1155/2012/569201
[15] Philos, ChG: Oscillation theorems for linear differential equations of second order. Arch. Math. 53, 482-492 (1989) · Zbl 0661.34030 · doi:10.1007/BF01324723
[16] Rogovchenko, YuV: Oscillation theorems for second-order equations with damping. Nonlinear Anal. 41, 1005-1028 (2000) · Zbl 0972.34022 · doi:10.1016/S0362-546X(98)00324-1
[17] Şenel, MT, Utku, N: Oscillation criteria for third-order neutral dynamic equations with continuously distributed delay. Adv. Differ. Equ. 2014, 220 (2014) · Zbl 1417.39035 · doi:10.1186/1687-1847-2014-220
[18] Tiryaki, A, Aktaş, MF: Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping. J. Math. Anal. Appl. 325, 54-68 (2007) · Zbl 1110.34048 · doi:10.1016/j.jmaa.2006.01.001
[19] Zhang, QX, Gao, L, Yu, YH: Oscillation criteria for third-order neutral differential equations with continuously distributed delay. Appl. Math. Lett. 25, 1514-1519 (2012) · Zbl 1253.34062 · doi:10.1016/j.aml.2012.01.007
[20] Wang, PG, Cai, H: Oscillatory criteria for higher order functional differential equations with damping. J. Funct. Spaces Appl. 2013, Article ID 968356 (2013). doi:10.1155/2013/968356 · Zbl 1269.34075 · doi:10.1155/2013/968356
[21] Erbe, LH, Kong, Q, Zhang, BG: Oscillation Theory for Functional Differential Equations. Dekker, New York (1995)
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