×

Asymptotic behavior of even-order damped differential equations with \(p\)-Laplacian like operators and deviating arguments. (English) Zbl 1355.34106

Summary: We study the asymptotic properties of the solutions of a class of even-order damped differential equations with \(p\)-Laplacian like operators, delayed and advanced arguments. We present new theorems that improve and complement related contributions reported in the literature. Several examples are provided to illustrate the practicability, maneuverability, and efficiency of the results obtained. An open problem is proposed.

MSC:

34K11 Oscillation theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hale, JK: Theory of Functional Differential Equations. Springer, New York (1977) · Zbl 0352.34001 · doi:10.1007/978-1-4612-9892-2
[2] Agarwal, RP, Grace, SR, O’Regan, D: Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations. Kluwer Academic Publishers, Dordrecht (2002) · Zbl 1073.34002 · doi:10.1007/978-94-017-2515-6
[3] Zhang, C, Agarwal, RP, Li, T: Oscillation and asymptotic behavior of higher-order delay differential equations with p-Laplacian like operators. J. Math. Anal. Appl. 409, 1093-1106 (2014) · Zbl 1314.34141 · doi:10.1016/j.jmaa.2013.07.066
[4] Agarwal, RP, Bohner, M, Li, T, Zhang, C: Oscillation of second-order Emden-Fowler neutral delay differential equations. Ann. Mat. Pura Appl. 193, 1861-1875 (2014) · Zbl 1308.34083 · doi:10.1007/s10231-013-0361-7
[5] Agarwal, RP, Grace, SR, O’Regan, D: Oscillation Theory for Difference and Functional Differential Equations. Kluwer Academic Publishers, Dordrecht (2000) · Zbl 0954.34002 · doi:10.1007/978-94-015-9401-1
[6] Bohner, M, Saker, SH: Oscillation of damped second order nonlinear delay differential equations of Emden-Fowler type. Adv. Dyn. Syst. Appl. 1, 163-182 (2006) · Zbl 1132.34046
[7] Erbe, L, Hassan, TS, Peterson, A: Oscillation criteria for nonlinear damped dynamic equations on time scales. Appl. Math. Comput. 203, 343-357 (2008) · Zbl 1162.39005
[8] Fišnarová, S, Mařík, R: Oscillation criteria for neutral second-order half-linear differential equations with applications to Euler type equations. Bound. Value Probl. 2014, 83 (2014) · Zbl 1307.34108 · doi:10.1186/1687-2770-2014-83
[9] Fu, X, Li, T, Zhang, C: Oscillation of second-order damped differential equations. Adv. Differ. Equ. 2013, 326 (2013) · Zbl 1391.34068 · doi:10.1186/1687-1847-2013-326
[10] Karpuz, B, Öcalan, Ö, Öztürk, S: Comparison theorems on the oscillation and asymptotic behaviour of higher-order neutral differential equations. Glasg. Math. J. 52, 107-114 (2010) · Zbl 1216.34073 · doi:10.1017/S0017089509990188
[11] Li, T, Rogovchenko, YuV: Asymptotic behavior of an odd-order delay differential equation. Bound. Value Probl. 2014, 107 (2014) · Zbl 1308.34098 · doi:10.1186/1687-2770-2014-107
[12] Li, T, Rogovchenko, YuV, Tang, S: Oscillation of second-order nonlinear differential equations with damping. Math. Slovaca 64, 1227-1236 (2014) · Zbl 1349.34111 · doi:10.2478/s12175-014-0271-1
[13] Liu, S, Zhang, Q, Yu, Y: Oscillation of even-order half-linear functional differential equations with damping. Comput. Math. Appl. 61, 2191-2196 (2011) · Zbl 1219.34045 · doi:10.1016/j.camwa.2010.09.011
[14] Philos, ChG: A new criterion for the oscillatory and asymptotic behavior of delay differential equations. Bull. Acad. Pol. Sci., Sér. Sci. Math. 39, 61-64 (1981) · Zbl 0482.34056
[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, Tuncay, F: Oscillation criteria for second-order nonlinear differential equations with damping. Nonlinear Anal. 69, 208-221 (2008) · Zbl 1147.34026 · doi:10.1016/j.na.2007.05.012
[17] Saker, SH, Agarwal, RP, O’Regan, D: Oscillation of second-order damped dynamic equations on time scales. J. Math. Anal. Appl. 330, 1317-1337 (2007) · Zbl 1128.34022 · doi:10.1016/j.jmaa.2006.06.103
[18] Thandapani, E, Murugadass, S, Pinelas, S: Oscillation criteria for second order nonlinear differential equations with damping and mixed nonlinearities. Funct. Differ. Equ. 17, 319-328 (2010) · Zbl 1235.34106
[19] Zhang, C, Li, T, Sun, B, Thandapani, E: On the oscillation of higher-order half-linear delay differential equations. Appl. Math. Lett. 24, 1618-1621 (2011) · Zbl 1223.34095 · doi:10.1016/j.aml.2011.04.015
[20] Zhang, Q: Oscillation of second-order half-linear delay dynamic equations with damping on time scales. J. Comput. Appl. Math. 235, 1180-1188 (2011) · Zbl 1207.34087 · doi:10.1016/j.cam.2010.07.027
[21] Zhang, Q, Liu, S, Gao, L: Oscillation criteria for even-order half-linear functional differential equations with damping. Appl. Math. Lett. 24, 1709-1715 (2011) · Zbl 1223.34096 · doi:10.1016/j.aml.2011.04.025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.