Lynn Erbe, Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0130, USA, e-mail: email@example.com; Raziye Mert, Department of Mathematics and Computer Science, Çankaya University, Eskişehir Yolu 29.km, 06810, Ankara , Turkey, e-mail: firstname.lastname@example.org; Allan Peterson, Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0130, USA, e-mail: email@example.com; Ağacık Zafer, Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey, e-mail: firstname.lastname@example.org
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.
Keywords: time scale, even order, delay, oscillation, Taylor monomial
Classification (MSC 2010): 34K11, 39A10, 39A99
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