Abstract
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.
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Erbe, L., Mert, R., Peterson, A. et al. Oscillation of even order nonlinear delay dynamic equations on time scales. Czech Math J 63, 265–279 (2013). https://doi.org/10.1007/s10587-013-0017-1
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DOI: https://doi.org/10.1007/s10587-013-0017-1