Oscillation of even order nonlinear delay dynamic equations on time scales

Lynn H. Erbe; Raziye Mert; Allan Peterson; Ağacık Zafer

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 1, page 265-279
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Erbe, Lynn H., et al. "Oscillation of even order nonlinear delay dynamic equations on time scales." Czechoslovak Mathematical Journal 63.1 (2013): 265-279. <http://eudml.org/doc/252521>.

@article{Erbe2013,
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.},
author = {Erbe, Lynn H., Mert, Raziye, Peterson, Allan, Zafer, Ağacık},
journal = {Czechoslovak Mathematical Journal},
keywords = {time scale; even order; delay; oscillation; Taylor monomial; time scale; even order; delay; oscillation; Taylor monomial},
language = {eng},
number = {1},
pages = {265-279},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of even order nonlinear delay dynamic equations on time scales},
url = {http://eudml.org/doc/252521},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Erbe, Lynn H.
AU - Mert, Raziye
AU - Peterson, Allan
AU - Zafer, Ağacık
TI - Oscillation of even order nonlinear delay dynamic equations on time scales
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 1
SP - 265
EP - 279
AB - 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.
LA - eng
KW - time scale; even order; delay; oscillation; Taylor monomial; time scale; even order; delay; oscillation; Taylor monomial
UR - http://eudml.org/doc/252521
ER -

References

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