# Article

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Keywords:
neutral differential equations; nonoscillation; oscillation; positive and negative coefficients
Summary:
In this paper, we study the existence of oscillatory and nonoscillatory solutions of neutral differential equations of the form $$x(t)-cx(t-r)$$'\pm$$P(t)x(t-\theta)-Q(t)x(t-\delta)$$=0 where $c>0$, $r>0$, $\theta>\delta\geq0$ are constants, and $P$, $Q\in C(\bb R^+\!,\bb R^+)$. We obtain some sufficient and some necessary conditions for the existence of bounded and unbounded positive solutions, as well as some sufficient conditions for the existence of bounded and unbounded oscillatory solutions.
References:
[1] D. D. Bainov D. P. Mishev: Oscillation Theory for Neutral Differential Equations with Delay. Adam Hilger, Philadelphia, 1991. MR 1147908
[2] Q. Chuanxi G. Ladas: Linearized oscillation for equations with positive, negative coefficients. Hiroshima Math. J. 20 (1990), 331-340. MR 1063367
[3] L. H. Erbe Q. Kong B. G. Zhang: Oscillation Theory for Functional Differential Equations. Marcel Dekker, New York, 1994. MR 1309905
[4] I. Györi G. Ladas: Oscillation Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford, 1991. MR 1168471
[5] J. Jaroš T. Kusano: Existence of oscillatory solutions for functional differential equations of neutral type. Acta Math. Univ. Comenian. 60 (1991), 185-194. MR 1155243
[6] G. Ladas C. Qian: Oscillation in differential equations with positive, negative coefficients. Canad. Math. Bull. 33 (1990), 442-451. DOI 10.4153/CMB-1990-072-x | MR 1091349
[7] B. S. Lalli B. G. Zhang: Oscillation of first order neutral differential equations. Appl. Anal. 39 (1990), 265-274. DOI 10.1080/00036819008839986 | MR 1095638
[8] Yu Jianshe, Wang Zhicheng: Some further results on oscillation of neutral differential equations. Bull. Austral. Math. Soc. 46 (1992), 147-154. MR 1170449 | Zbl 0729.34051
[9] Yu Jianshe: On the neutral delay differentia! equation with positive, negative coefficients. Acta. Math. Sinica 34 (1991), 517-523. MR 1152147
[10] B. G. Zhang J. S. Yu: The existence of positive solutions of neutral differential equations. Scientia Sinica 8 (1992), 785-790.

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