Geodesic
Oscillation of even order nonlinear delay dynamic equations on time scales
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 265-279.

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One of the important methods for studying the oscillation of higher order differential equations is to make a comparison with second order differential equations. The method involves using Taylor's Formula. In this paper we show how such a method can be used for a class of even order delay dynamic equations on time scales via comparison with second order dynamic inequalities. In particular, it is shown that nonexistence of an eventually positive solution of a certain second order delay dynamic inequality is sufficient for oscillation of even order dynamic equations on time scales. The arguments are based on Taylor monomials on time scales.
DOI : 10.1007/s10587-013-0017-1
Classification : 34K11, 34N05, 39A10, 39A99
Keywords: time scale; even order; delay; oscillation; Taylor monomial 
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Erbe, Lynn; Mert, Raziye; Peterson, Allan; Zafer, Ağacık. Oscillation of even order nonlinear delay dynamic equations on time scales. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 265-279. doi : 10.1007/s10587-013-0017-1. http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0017-1/

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