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Oscillation of second-order nonlinear neutral differential equations. (English) Zbl 1085.34053

The equation
\[ x(t)-p(t)x(t-\tau)''+q(t) f(x(t-\sigma))=0 \]
has a bounded eventually positive solution or every solution is oscillatory under certain conditions when \(f(x)\) is superlinear. For sublinear case, the equation has an eventually positive solution which tends to infinity or every solution is oscillatory.

MSC:

34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
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References:

[1] Atkinson, F. V., On second-order nonlinear oscillation, Pacific J. Math., 5, 643-647 (1955) · Zbl 0065.32001
[2] Belohorec, S., Oscillations solutions of certern nonlinear differential equations of second-order, Mat. Fyz. Casopis Sloven Akad. Vied., 11, 250-255 (1961) · Zbl 0108.09103
[3] Erbe, L. H.; Kong, Q.; Zhang, B. G., Oscillation Theory for Functional Differential Equations (1995), Dekker: Dekker New York
[4] Györi, I.; Ladas, G., Oscillation Theory of Delay Differential Equations With Applications (1991), Clarendon: Clarendon Oxford · Zbl 0780.34048
[5] Li, H. J.; Liu, W. L., Oscillations of second-order neutral differential equations, Math. Comput. Modelling, 22, 45-53 (1995) · Zbl 0833.34066
[6] Jiang, J.; Li, X., Oscillation of second-order nonlinear neutral differential equations, Appl. Math. Comput., 135, 531-540 (2003) · Zbl 1026.34081
[7] Ladas, G.; Partheniadis, E. C.; Sficas, Y. G., Oscillations of second-order neutral equations, Canad. J. Math., 41, 1301-1314 (1988) · Zbl 0666.34078
[8] Ladas, G.; Partheniadis, E. C.; Sficas, Y. G., Necessary and sufficient conditions for oscillations of second-order neutral equations, J. Math. Anal. Appl., 138, 214-231 (1989) · Zbl 0668.34069
[9] Sahiner, Y., On oscillation of second-order neutral type delay differential equations, Appl. Math. Comput., 150, 697-706 (2004) · Zbl 1045.34038
[10] Tanaka, S., A oscillation theorem for a class of even order neutral differential equations, J. Math. Anal. Appl., 273, 172-189 (2002) · Zbl 1022.34065
[11] Tang, X. H., Oscillation for first order nonlinear delay differential equations, J. Math. Anal. Appl., 264, 510-521 (2001) · Zbl 1001.34058
[12] Tang, X. H., Oscillation for first order superlinear delay differential equations, J. London Math. Soc., 65, 115-122 (2002) · Zbl 1024.34058
[13] Wong, J. S.W., Necessary and sufficient conditions for oscillation of second-order neutral differential equations, J. Math. Anal. Appl., 252, 342-352 (2000) · Zbl 0976.34057
[14] Yan, J., Oscillations of second-order neutral functional differential equations, Appl. Math. Comput., 83, 27-41 (1997) · Zbl 0868.34060
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