Oscillation results for second-order nonlinear neutral delay dynamic equations on time scales

Abstract

In this article, we consider the second-order nonlinear neutral delay dynamic equation

on a time scale and establish some new oscillation and nonoscillation criteria. Also from these we deduce the Leighton–Wintner, Hille–Kneser, Kamenev, and Philos types oscillation criteria. Our results are different and complement the existence oscillation results for neutral delay dynamic equations on time scales in (Agarwal et al. 2004, Oscillation criteria for second-order nonlinear neutral dynamic equations. Journal of Mathematical Analysis and Applications, 300, 203–217) and (S.H. Saker, 2006, Oscillation of second-order nonlinear neutral delay dynamic equations on time scales. Journal of Computational and Applied Mathematics, 187, 123–141). Our results can be applied on the time scales , , , for h > 0, , , , and when where {t _n } is the set of harmonic numbers, etc. Some examples are considered to illustrate the main results.

Keywords:

• Oscillation
• Second-order neutral nonlinear dynamic equation
• Time scales

Keywords:

• 2000 AMS Subject Classifications: 34K11
• 39A10
• 39A99 (34A99; 34C10; 39A11)