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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 of functional-differential equations
Full Text:
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) [3] Erbe, L. H.; Kong, Q.; Zhang, B. G.: Oscillation theory for functional differential equations. (1995) · Zbl 0821.34067 [4] Györi, I.; Ladas, G.: Oscillation theory of delay differential equations with applications. (1991) · 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