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Asymptotic dichotomy in a class of fourth-order nonlinear delay differential equations with damping. (English) Zbl 1173.34350

Summary: All solutions of a fourth-order nonlinear delay differential equation are shown to converge to zero or to oscillate. Novel Riccati type techniques involving third-order linear differential equations are employed. Implications in the deflection of elastic horizontal beams are also indicated.

MSC:

34K25 Asymptotic theory of functional-differential equations
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References:

[1] A. Tiryaki and M. F. Akta\cs, “Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping,” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 54-68, 2007. · Zbl 1110.34048
[2] G. S. Ladde, V. Lakshmikantham, and B. G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, vol. 110 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1987. · Zbl 0832.34071
[3] Z. G. Ouyang and Y. K. Li, “Monotone solutions of even-order delay differential equations,” Journal of Mathematical Research and Exposition, vol. 24, no. 2, pp. 321-327, 2004. · Zbl 1051.34055
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