Agarwal, Ravi P.; Grace, Said R.; Manojlovic, Jelena V. Oscillation criteria for certain fourth order nonlinear functional differential equations. (English) Zbl 1137.34031 Math. Comput. Modelling 44, No. 1-2, 163-187 (2006). Summary: Some new criteria for the oscillation of the fourth-order functional-differential equation\[ \frac{d}{dt} \left( \frac{1}{a_3(t)} \left( \frac{d}{dt} \frac{1}{a_2(t)} \left( \frac{d}{dt} \frac{1}{a_1(t)} \left( \frac{d}{dt} x(t)\right)^{\alpha_1} \right)^{\alpha_2} \right)^{\alpha_3}\right)+ \delta q(t) f(x[g(t)])=0, \]where \(\delta=\pm1\) are established. Cited in 19 Documents MSC: 34K11 Oscillation theory of functional-differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations Keywords:nonoscillation; comparison PDFBibTeX XMLCite \textit{R. P. Agarwal} et al., Math. Comput. Modelling 44, No. 1--2, 163--187 (2006; Zbl 1137.34031) Full Text: DOI References: [1] Agarwal, R. P.; Grace, S. R.; O’Regan, D., Oscillation Theory for Difference and Functional Differential Equations (2000), Kluwer: Kluwer Dordrecht · Zbl 0969.34062 [2] Agarwal, R. P.; Grace, S. R.; O’Regan, D., Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations (2002), Kluwer: Kluwer Dordrecht · Zbl 1073.34002 [3] Agarwal, R. P.; Grace, S. R.; O’Regan, D., Oscillation Theory for Second Order Dynamic Equations (2003), Taylor & Francis: Taylor & Francis UK · Zbl 1070.34083 [4] Agarwal, R. P.; Grace, S. R.; O’Regan, D., On the oscillation of certain functional differential equations via comparison methods, J. Math. Anal. Appl., 286, 577-600 (2003) · Zbl 1057.34072 [5] Agarwal, R. P.; Grace, S. R.; O’Regan, D., The oscillation of certain higher order functional differential equations, Math. Comput. Modelling, 37, 705-728 (2003) · Zbl 1070.34083 [6] Agarwal, R. P.; Grace, S. R.; O’Regan, D., On the oscillation of second order functional differential equations, Adv. Math. Sci. Appl., 12, 257-272 (2002) · Zbl 1041.34052 [7] Agarwal, R. P.; Grace, S. R.; O’Regan, D., Nonoscillatory solutions for higher order dynamic equations, J. London Math. Soc., 67, 165-179 (2003) · Zbl 1050.34093 [8] Agarwal, R. P.; Grace, S. R.; O’Regan, D., Oscillation criteria for certain \(n\) th order differential equations with deviating arguments, J. Math. Anal. Appl., 262, 601-622 (2001) · Zbl 0997.34060 [9] Agarwal, R. P.; Grace, S. R., Oscillation of certain functional differential equations, Comput. Math. Appl., 38, 143-153 (1999) · Zbl 0935.34059 [10] Agarwal, R. P.; Grace, S. R., On the oscillation of higher order differential equations with deviating arguments, Comput. Math. Appl., 38, 185-199 (1999) · Zbl 0935.34058 [11] Györi, I.; Ladas, G., Oscillation Theory of Delay Differential Equations with Applications (1991), Oxford Univ. Press: Oxford Univ. Press Oxford · Zbl 0780.34048 [12] Kusano, T.; Lalli, B. S., On oscillation of half-linear functional differential equations with deviating arguments, Hiroshima Math. J., 24, 549-563 (1994) · Zbl 0836.34081 [13] Philos, Ch. G., On the existence of nonoscillatory solutions tending to zero at \(\infty\) for differential equations with positive delays, Arch. Math., 36, 168-178 (1981) · Zbl 0463.34050 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.