1074-34-94
Raziye Mert* (raziyemert@cankaya.edu.tr), Cankaya University, Department of Mathematics,
and Computer Science, 06530 Ankara, Ankara, Turkey, and Ağacık Zafer. Oscillation of Even
Order Nonlinear Delay Dynamic Equations on Time Scales.
This is a joint work with Ağacık Zafer. 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
series expansion of solutions. In this talk 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 suffcient for
oscillation of even order dynamic equations on time scales. The arguments are based on Taylor polynomials on time
scales. (Received August 12, 2011)
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