Parhi, N.; Tripathy, A. K. On oscillatory fourth order nonlinear neutral differential equations. II. (English) Zbl 1114.34048 Math. Slovaca 55, No. 2, 183-202 (2005). [For part I see ibid. 54, No. 4, 389–410 (2004; Zbl 1099.34061).] The authors study the oscillatory behaviour of solutions to the fourth order neutral differential equation\[ \bigl [r(t)\big (y(t)+p(t)\,y(t-\tau )\big )''\bigr ]''+q(t)\,G\big (y(t-\sigma ) \big )=0 \]and the associated forced equation \[ \bigl [r(t)\big (y(t)+p(t)\,y(t-\tau )\big )''\bigr ]''+q(t)\,G\big (y(t-\sigma ) \big )=f(t) \]under the assumption \(\int _0^\infty \bigl (t/r(t)\bigr )\,dt=\infty \) for various ranges of \(p(t)\). Sufficient conditions for the existence of bounded positive solutions to the forced equation are obtained too. Reviewer: Igor Bock (Bratislava) Cited in 6 Documents MSC: 34K11 Oscillation theory of functional-differential equations 34K12 Growth, boundedness, comparison of solutions to functional-differential equations 34K40 Neutral functional-differential equations Keywords:oscillation; nonoscillation; neutral differential equation; existence of positive solutions, asymptotic behaviour Citations:Zbl 1099.34061 PDF BibTeX XML Cite \textit{N. Parhi} and \textit{A. K. Tripathy}, Math. Slovaca 55, No. 2, 183--202 (2005; Zbl 1114.34048) Full Text: EuDML 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] KUSANO T.-NAITO M.: On fourth order non-linear oscillations. J. London Math. Soc. (2) 14 (1976), 91-105. · Zbl 0385.34014 [4] 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 [5] PARHI N.-RATH R. N.: On oscillation criteria for forced non-linear higher order neutral differential equations. Math. Slovaca 54 (2004), 369-388. · Zbl 1099.34060 [6] PARHI N.-TRIPATHY A. K.: On oscillatory fourth order non-linear neutral differential equations I. Math. Slovaca 54 (2004), 389-410. · Zbl 1099.34061 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.