New results of oscillation for certain second-order nonlinear dynamic equations on time scales

doi:10.3969/j.issn.1000-5641.2017.03.006

Abstract

Abstract:

This paper is concerned with oscillatory behavior of the following second-order nonlinear neutral variable delay functional dynamic equations

[A（t）Φ（[x（t）+B（t）g（x（τ（t）））]^Δ）]^Δ+ƒ（t，x（δ（t）））=0

on a time scale T, where Φ（u）=|u|^λ-1u (hereλ> 0 is an arbitrary constant). By using a couple of Riccati substitutions, the time scales theory and inequality technique, we establish two new oscillation criteria for the equations, these results deal with some cases not covered by existing results in the literature. Finally, two examples are presented to illustrate the importance of our theorems.

Key words: oscillation, time scales, functional dynamic equations, variable delay

CLC Number:

O175.7

YANG Jia-shan, ZHANG Xiao-jian. New results of oscillation for certain second-order nonlinear dynamic equations on time scales[J]. Journal of East China Normal University(Natural Sc, 2017, (3): 54-63.

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