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neutral equation; mixed argument
The aim of this paper is to present new oscillatory criteria for the second order neutral differential equation with mixed argument \[ (x(t)-px(t-\tau ))^{\prime \prime }- q(t)x(\sigma (t))=0. \] The results include also sufficient conditions for bounded and unbounded oscillation of the equations considered.
[1] D. D. Bainov, D. P. Mishev: Oscillation Theory for Neutral Differential Equations with Delay. Adam Hilger, 1991. MR 1147908
[2] T. A. Chanturia, R. G. Koplatadze: On Oscillatory Properties of Differential Equations with Deviating Arguments. Tbilisi, Univ. Press, Tbilisi, 1977. (Russian)
[3] J. Dzurina, B. Mihalikova: A note on unstable neutral differential equations of the second order. Math. Fascic. 29 (1999), 17–22. MR 1724462
[4] L. H. Erbe, Q. Kong, B. G. Zhang: Oscillation Theory for Functional Differential Equations. Marcel Dekker, New York, 1995. MR 1309905
[5] I. Győri, G. Ladas: Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford, 1991. MR 1168471
[6] G. S. Ladde, V. Lakshmikantham, B. G. Zhang: Oscillation Theory of Differential Equations with Deviating Arguments. Dekker, New York, 1987. MR 1017244
[7] J. S. Yu, Z. C. Wang: Some further result on oscillation of neutral differential equations. Bull. Austral. Math. Soc. 46 (1992), 149–157. DOI 10.1017/S0004972700011758 | MR 1170449
[8] J. S. Yu, B. G. Zhang: The existence of positive solution and bounded oscillation for second-order neutral differential equations of unstable type. J. Syst. Sci. Math. 16 (1996), 92–96. MR 1404160
[9] B. G. Zhang: Oscillation of second order neutral differential equations. Kexue Tongbao 34 (1989), 563–566. MR 1020422 | Zbl 0661.34074
[10] B. G. Zhang, J. S. Yu: On the existence of asymptotically decaying positive solutions of second order neutral differential equations. J. Math. Anal. Appl. 166 (1992), 1–11. DOI 10.1016/0022-247X(92)90322-5 | MR 1159633 | Zbl 0754.34075
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