Oscillation of even order nonlinear delay dynamic equations on time scales |
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Authors: | Lynn Erbe Raziye Mert Allan Peterson Ağacık Zafer |
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Institution: | 117. Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, 68588-0130, USA 217. Department of Mathematics and Computer Science, ?ankaya University, Eski?ehir Yolu 29.km, 06810, Ankara, Turkey 317. Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey
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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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