Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale

Year, pages: 2016, 185 - 196

In this paper, we consider the oscillation for the second-order quasi-linear neutral dynamic equation

$$ (r(t)|Z^Δ(t)|^α-1Z^Δ(t))^Δ +q(t)|x(δ(t))|^β-1x(δ(t))=0. $$

on time scale $\T$, where $Z(t)=x(t)+p(t)x(τ(t))$, $α,β>0$ are constants. We establish some new oscillation criteria and give sufficient conditions to insure that all solutions of quasi-linear neutral dynamic equation are oscillatory on time scale $\mathbb{T}$. The new oscillation criteria are presented that improve some known results in the literature.

Yang, Q., Xu, Z., Long, P. 2016. Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale. In Mathematica Slovaca, vol. 66, no.1, pp. 185-196. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0128

Yang, Q., Xu, Z., Long, P. (2016). Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale. Mathematica Slovaca, 66(1), 185-196. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0128