Geodesic
On unstable neutral differential equations of the second order
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 4, pp. 739-747

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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.
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.
Classification : 34C10, 34K11, 34K20, 34K40
Keywords: neutral equation; delayed argument 
Džurina, Jozef. On unstable neutral differential equations of the second order. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 4, pp. 739-747. http://geodesic.mathdoc.fr/item/CMJ_2002_52_4_a6/
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     zbl = {1023.34057},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2002_52_4_a6/}
}
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[1] D. D. Bainov and D. P. Mishev: Oscillation Theory for Neutral Differential Equations with Delay. Adam Hilger, Bristol, 1991. | MR

[2] T. A. Čanturia and R. G. Koplatadze: On oscillatory properties of differential equations with deviating arguments. Tbilisi, Univ. Press, Tbilisi, 1977. (Russian)

[3] L. H. Erbe, Q. Kong and B. G. Zhang: Oscillation Theory for Functional Differential Equations. Dekker, New York, 1995. | MR

[4] I. Győri and G. Ladas: Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford, 1991. | MR

[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. | DOI | MR

[6] G. S. Ladde, V. Lakshmikantham and B. G. Zhang: Oscillation theory of differential equations with deviating arguments. Dekker, New York, 1987. | MR

[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. | DOI | MR

[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).

[9] B.G. Zhang: Oscillation of second order neutral differential equations. Kexue Tongbao 34 (1989), 563–566. | MR | Zbl

[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. | DOI | MR