Abstract
This paper is concerned with some oscillation criteria for the second order neutral delay dynamic equations with mixed nonlinearities of the form where and with . Further the results obtained here generalize and complement to the results obtained by Han et al. (2010). Examples are provided to illustrate the results.
Highlights
Since the introduction of time scale calculus by Stefan Hilger in 1988, there has been great interest in studying the qualitative behavior of dynamic equations on time scales, see, for example, 1–3 and the references cited therein
This paper is concerned with some oscillation criteria for the second order neutral delay dynamic equations with mixed nonlinearities of the form rtutΔqt |x τ t |α−1x τ t n i qi t
In 2004, Agarwal et al 5 have obtained some sufficient conditions for the oscillation of all solutions of the second order nonlinear neutral delay dynamic equation rtytptyt − τΔγΔft, y t − δ
Summary
Since the introduction of time scale calculus by Stefan Hilger in 1988, there has been great interest in studying the qualitative behavior of dynamic equations on time scales, see, for example, 1–3 and the references cited therein. This paper is concerned with some oscillation criteria for the second order neutral delay dynamic equations with mixed nonlinearities of the form rtutΔqt |x τ t |α−1x τ t n i qi t
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