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Oscillation of second order nonlinear neutral differential equations. (English) Zbl 1026.34081
Summary: Consider the second-order nonlinear neutral delay differential equation $$\Bigl[r(t) \biggl(\bigl(x(t)+ p(t)x(t-\tau)\bigr)' \biggr)^\alpha \Bigr]'+f \bigl(t,x(t- \sigma)\bigr) =0,\tag E$$ where $\tau$ and $\sigma$ are nonnegative constants, and $\alpha$ is a quotient of positive odd integers. Some new oscillatory criteria for (E) are established. Several examples which dwell upon the importance of our results are illustrated, too.

##### MSC:
 34K11 Oscillation theory of functional-differential equations 34K40 Neutral functional-differential equations
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##### References:
 [1] Hartman, P.: Ordinary differential equations. (1982) · Zbl 0476.34002 [2] Grammatikopoules, M. K.; Ladas, G.; Meimaridou, A.: Oscillation of second order neutral delay differential equations. Rat. math. 1, 267-274 (1985) · Zbl 0581.34051 [3] Ruan, S.: Oscillation of second order neutral differential equations. Canad. math. Bull. 36, 485-496 (1993) · Zbl 0798.34079 [4] Philos, C. G.: Oscillation theorems for linear differential equation of second order. Arch. math. 53, 483-492 (1989) · Zbl 0661.34030 [5] Li, H. J.; Liu, W. L.: Oscillation criteria for second order neutral differential equations. Canad. J. Math. 48, 871-886 (1996) · Zbl 0859.34055 [6] Lou, J. W.: Oscillation of second order nonlinear neutral differential equations. J. shaoying teachers college 20, No. 5, 17-25 (1998) [7] Jiang, J. C.: Oscillation and nonoscillation theorems for second order nonlinear differential equations. Tamkang. J. Math. 32, No. 2, 95-102 (2001) · Zbl 0999.34038 [8] Wang, J. F.: On second order quasilinear oscillations. Funkcial. ekvac. 41, 25-54 (1998) · Zbl 1140.34356 [9] Del Pino, M.; Manasevich, R.: Some nonlinear Sturmian comparison theory for (|u’|p-2u’)’+$c(t)$|u|p-$2{\cdot}$u=0. Lecture notes in pure and applied mathematics 118, 183-190 (1989)