Oscillation of even order nonlinear delay dynamic equations on time scales

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Erbe L., Mert R., Peterson A., Zafer A.

CZECHOSLOVAK MATHEMATICAL JOURNAL, vol.63, no.1, pp.265-279, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.1007/s10587-013-0017-1
  • Journal Name: CZECHOSLOVAK MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.265-279
  • Middle East Technical University Affiliated: Yes

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.