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On oscillatory fourth order nonlinear neutral differential equations I. (English) Zbl 1099.34061
Summary: Here, oscillatory and asymptotic properties of solutions of the classes of fourth order neutral differential equations $\bigl (r(t)\bigl (y(t)+p(t) y(t-\tau)\bigr)''\bigr)'' + q(t) G \bigl (y(t - \sigma)\bigr) = f(t) \tag{*}$ and $\bigl (r(t)\bigl (y(t)+p(t)y(t-\tau)\bigr)''\bigr)'' + q(t) G \bigl (y(t - \sigma)\bigr) = 0$ are studied under the assumption $$\int _0^\infty \frac t{r(t)}\,\operatorname {d}\!t<\infty$$ for various ranges of $$p(t)$$. Sufficient conditions are obtained for the existence of bounded positive solutions of equation (*).

##### MSC:
 34K11 Oscillation theory of functional-differential equations 34K25 Asymptotic theory of functional-differential equations 34K12 Growth, boundedness, comparison of solutions to functional-differential equations 34K40 Neutral functional-differential equations
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##### References:
 [1] GYORI I.-LADAS G.: Oscillation Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford, 1991. [2] KUSANO T.-NAITO M.: Non linear oscillation of fourth order differential equations. Canad. J. Math. 4 (1976), 840-852. · Zbl 0432.34022 [3] PARHI N.-RATH R. N.: On oscillation of solutions of forced non linear neutral differential equations of higher order. Czechoslovak Math. J. · Zbl 1080.34522 [4] PARHI N.-RATH R. N.: On oscillation criteria for forced nonlinear higher order neutral differential equations. · Zbl 1099.34060
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