Czechoslovak Mathematical Journal, Vol. 63, No. 1, pp. 265-279, 2013

Oscillation of even order nonlinear delay dynamic equations on time scales

Lynn Erbe, Raziye Mert, Allan Peterson, Ağacık Zafer

Lynn Erbe, Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0130, USA, e-mail: lerbe2@math.unl.edu; Raziye Mert, Department of Mathematics and Computer Science, Çankaya University, Eskişehir Yolu 29.km, 06810, Ankara , Turkey, e-mail: raziyemert@cankaya.edu.tr; Allan Peterson, Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0130, USA, e-mail: apeterson1@math.unl.edu; Ağacık Zafer, Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey, e-mail: zafer@metu.edu.tr

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


Full text available as PDF.

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
Subscribers of Springer need to access the articles on their site, which is http://link.springer.com/journal/10587.


[Previous Article] [Next Article] [Contents of This Number] [Contents of Czechoslovak Mathematical Journal]