Lin, Xiaoyan Oscillation of second-order nonlinear neutral differential equations. (English) Zbl 1085.34053 J. Math. Anal. Appl. 309, No. 2, 442-452 (2005). 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. Reviewer: R. S. Dahiya (Ames) Cited in 22 Documents MSC: 34K11 Oscillation theory of functional-differential equations 34K40 Neutral functional-differential equations 34K12 Growth, boundedness, comparison of solutions to functional-differential equations Keywords:Neutral differential equation; Second-order; Superlinear; Sublinear; Oscillation; Nonoscillation PDFBibTeX XMLCite \textit{X. Lin}, J. Math. Anal. Appl. 309, No. 2, 442--452 (2005; Zbl 1085.34053) Full Text: DOI 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 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.