Oscillation criteria for quasi-linear functional dynamic equations on time scales

Rok, strany: 2012, 501 - 524

This paper is concerned with oscillation of the second-order quasi-linear functional dynamic equation

$$ (r(t)(x^Δ(t))^γ)^Δ +p(t)x^β(τ(t))=0, $$

on a time scale $\mathbb{T}$ where $γ$ and $β$ are quotient of odd positive integers, $r$, $p$, and $τ$ are positive rd-continuous functions defined on $\mathbb{T}$, $τ :\mathbb{T}\rightarrow \mathbb{T}$ and $\lim_{t\rightarrow ∞}τ(t)=∞$. We establish some new sufficient conditions which ensure that every solution oscillates or converges to zero. Our results improve the oscillation results in the literature when $γ=β$, and $τ(t)≤ t$ and when $τ(t)>t$ the results are essentially new. Some examples are considered to illustrate the main results.

ISO 690:

Saker, S., Grace, S. 2012. Oscillation criteria for quasi-linear functional dynamic equations on time scales. In Mathematica Slovaca, vol. 62, no.3, pp. 501-524. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0026-9

APA:

Saker, S., Grace, S. (2012). Oscillation criteria for quasi-linear functional dynamic equations on time scales. Mathematica Slovaca, 62(3), 501-524. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0026-9