New oscillation criteria for third order nonlinear neutral difference equations

Year, pages: 2011, 579 - 600

In this paper, we are concerned with oscillation of the third-order nonlinear neutral difference equation

$$ Δ(c_n[Δ(d_nΔ(x_n+p_nx_n-τ))]^γ) +q_nf(x_g(n))=0,    n≥ n₀, $$

where $γ >0$ is the quotient of odd positive integers, $c_n$, $d_n$, $p_n$ and $q_n$ are positive sequences of real numbers, $τ$ is a nonnegative integer, $g(n)$ is a sequence of nonnegative integers and $f\in C(\mathbb{R,R)}$ such that $uf(u)>0$ for $u\neq 0$. Our results extend and improve some previously obtained ones. Some examples are considered to illustrate the main results.

Saker, S. 2011. New oscillation criteria for third order nonlinear neutral difference equations. In Mathematica Slovaca, vol. 61, no.4, pp. 579-600. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0030-5

Saker, S. (2011). New oscillation criteria for third order nonlinear neutral difference equations. Mathematica Slovaca, 61(4), 579-600. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0030-5