Previous |  Up |  Next


neutral equation; delayed argument
In this paper we present some new oscillatory criteria for the $n$-th order neutral differential equations of the form \[ (x(t)\pm p(t)x[\tau (t)])^{(n)} +q(t)x[\sigma (t)] =0. \] The results obtained extend and improve a number of existing criteria.
[1] D. D.  Bainov and D. P.  Mishev: Oscillation Theory for Neutral Differential Equations with Delay. Adam Hilger, 1991. MR 1147908
[2] M. Budincevic: Oscillation of second order neutral nonlinear differential equations. Novi Sad J.  Math. 27 (1997), 49–56. MR 1660956 | Zbl 1074.34500
[3] I. T.  Kiguradze and T. A.  Chanturia: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations. Nauka, Moscow, 1991. (Russian)
[4] L. H.  Erbe and Q. Kong: Oscillation results for second order neutral differential equations. Funkc. Ekvacioj 35 (1992), 545–557. MR 1199473
[5] Q.  Chuanxi and G.  Ladas: Oscillations of higher order neutral differential equations with variable coefficients. Math. Nachr. 150 (1991), 15–24. DOI 10.1002/mana.19911500103 | MR 1109642
[6] S. R.  Gracem and B. S.  Lalli: Oscillation and asymptotic behavior of certain second order neutral differential equations. Radovi Mat. 5 (1989), 121–126. MR 1012728
[7] M. K.  Grammatikopoulos, G.  Ladas and A. Meimaridou: Oscillation and asymptotic behavior of higher order neutral equations with variable coefficients. Chinese Ann. Math. 9B (1988), 322–338. MR 0968469
[8] K.  Gopalsamy, B. S.  Lalli and B. G. Zhang: Oscillation of odd order neutral differential equations. Czechoslovak Math.  J. 42(117) (1992), 313–323. MR 1179502
[9] I. Győri and G.  Ladas: Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford, 1991. MR 1168471
[10] J. Hale: Theory of Functional Differential Equations. Springer-Verlag, New York, 1977. MR 0508721 | Zbl 0352.34001
[11] Š. Kulcsár: On the asymptotic behavior of the second order neutral differential equations. Publ. Math. Debrecen 57 (2000), 153–161.
[12] N.  Parhi and P. K.  Mohanty: Oscillation of neutral differential equations of higher order. Bull. Inst. Math. Sinica 24 (1996), 139–150.
[13] M.  Růžičková and E.  Špániková: Comparison theorems for differential equations of neutral type. Fasc. Math. (1998), 141–148.
Partner of
EuDML logo