# Article

 Title: On unstable neutral differential equations of the second order  (English) Author: Džurina, Jozef Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 Volume: 52 Issue: 4 Year: 2002 Pages: 739-747 Summary lang: English . Category: math . Summary: The aim of this paper is to present sufficient conditions for all bounded solutions of the second order neutral differential equation $\big (x(t)-px(t-\tau )\big )^{\prime \prime }- q(t)x\big (\sigma (t)\big )=0$ to be oscillatory and to improve some existing results. The main results are based on the comparison principles. Keyword: neutral equation Keyword: delayed argument MSC: 34C10 MSC: 34K11 MSC: 34K20 MSC: 34K40 idZBL: Zbl 1023.34057 idMR: MR1940055 . Date available: 2009-09-24T10:56:13Z Last updated: 2012-05-31 Stable URL: http://hdl.handle.net/10338.dmlcz/127760 . Reference: [1] D. D. Bainov and D. P. Mishev: Oscillation Theory for Neutral Differential Equations with Delay.Adam Hilger, Bristol, 1991. MR 1147908 Reference: [2] T. A. Čanturia and R. G. Koplatadze: On oscillatory properties of differential equations with deviating arguments.Tbilisi, Univ. Press, Tbilisi, 1977. (Russian) Reference: [3] L. H. Erbe, Q. Kong and B. G. Zhang: Oscillation Theory for Functional Differential Equations.Dekker, New York, 1995. MR 1309905 Reference: [4] I. Győri and G. Ladas: Theory of Delay Differential Equations with Applications.Clarendon Press, Oxford, 1991. MR 1168471 Reference: [5] J. Jaros and T. Kusano: Sufficient conditions for oscillations in higher order linear functional differential equations of neutral type.Japan. J. Math. 15 (1989), 415–432. MR 1039249 Reference: [6] G. S. Ladde, V. Lakshmikantham and B. G. Zhang: Oscillation theory of differential equations with deviating arguments.Dekker, New York, 1987. MR 1017244 Reference: [7] J. S. Yu and Z. C. Wang: Some further result on oscillation of neutral differential equations.Bull. Austral. Math. Soc. 46 (1992), 149–157. MR 1170449 Reference: [8] J. S. Yu and B. G. Zhang: The existence of positive solution for second order neutral differential equations with unstable type.Systems Sci. Math. Sci (to appear). Reference: [9] B.G. Zhang: Oscillation of second order neutral differential equations.Kexue Tongbao 34 (1989), 563–566. Zbl 0661.34074, MR 1020422 Reference: [10] B.G. Zhang and 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. MR 1159633 .

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