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.
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

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