Oscillation criteria for nonlinear neutral functional dynamic equations on time scales

Rok, strany: 2013, 263 - 290

In this paper, we establish some new sufficient conditions for oscillation of the second-order neutral functional dynamic equation

$$ [r(t)[m(t)y(t)+p(t)y(τ (t))]^Δ]^Δ+q(t)f(y(δ (t)))=0 $$

on a time scale $\mathbb{T}$ which is unbounded above, where $m$, $p$, $q$, $r$, $τ$ and $δ$ are real valued $rd$-continuous positive functions defined on $\mathbb{T}$. The main investigation of the results depends on the Riccati substitutions and the analysis of the associated Riccati dynamic inequality. The results complement the oscillation results for neutral delay dynamic equations and improve some oscillation results for neutral delay differential and difference equations. Some examples illustrating our main results are given.

ISO 690:

Kubiaczyk, I., Saker, S., Sikorska-Nowak, A. 2013. Oscillation criteria for nonlinear neutral functional dynamic equations on time scales. In Mathematica Slovaca, vol. 63, no.2, pp. 263-290. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0097-7

APA:

Kubiaczyk, I., Saker, S., Sikorska-Nowak, A. (2013). Oscillation criteria for nonlinear neutral functional dynamic equations on time scales. Mathematica Slovaca, 63(2), 263-290. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0097-7