Asymptotic behavior in neutral difference equations with negative coefficients

Year, pages: 2014, 391 - 402

In this paper, we study the asymptotic behavior of the solutions of a neutral difference equation of the form \begin{equation*} Δ [x(n)+cx(τ(n))]-p(n)x(σ(n))=0, \end{equation*} where $τ(n)$ is a general retarded argument, $σ(n)$ is a general deviated argument, $c\in \mathbb{R}$, $(-p(n))_{n≥ 0}$ is a sequence of negative real numbers such that $p(n)≥ p$, $p\in\mathbb{R}₊$, and $Δ$ denotes the forward difference operator $Δ x(n)=x(n+1)-x(n)$.

Chatzarakis, G., Miliaras, G. 2014. Asymptotic behavior in neutral difference equations with negative coefficients. In Mathematica Slovaca, vol. 64, no.2, pp. 391-402. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0212-z

Chatzarakis, G., Miliaras, G. (2014). Asymptotic behavior in neutral difference equations with negative coefficients. Mathematica Slovaca, 64(2), 391-402. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0212-z