On oscillatory fourth order nonlinear neutral differential equations. II. (English) Zbl 1114.34048

[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.


34K11 Oscillation theory of functional-differential equations
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
34K40 Neutral functional-differential equations


Zbl 1099.34061
Full Text: EuDML


[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
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