Asymptotic behavior of higher-order neutral difference equations with general arguments

  • G. E. Chatzarakis School Ped. and Technol. Education, Athens, Greece
  • H. Khatibzadeh Univ. Zanjan, Iran
  • G. N. Miliaras Amer. Univ. Athens, Greece
  • I. P. Stavroulakis Univ. Ioannina, Greece

Abstract

We study the asymptotic behavior of solutions of the higher-order neutral difference equation $$Δm[x(n)+cx(τ(n))]+p(n)x(σ(n))=0,N∍m≥2,n≥0,$$ where $τ (n)$ is a general retarded argument, $σ(n)$ is a general deviated argument, $c ∈ R; (p(n)) n ≥ 0$ is a sequence of real numbers, $∆$ denotes the forward difference operator $∆x(n) = x(n+1) - x(n)$; and $∆^j$ denotes the jth forward difference operator $∆^j (x(n) = ∆ (∆^{j-1}(x(n)))$ for $j = 2, 3,…,m$. Examples illustrating the results are also given.
Published
25.03.2013
How to Cite
ChatzarakisG. E., KhatibzadehH., MiliarasG. N., and StavroulakisI. P. “Asymptotic Behavior of Higher-Order Neutral Difference Equations With General Arguments”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 3, Mar. 2013, pp. 430-5, http://umj.imath.kiev.ua/index.php/umj/article/view/2429.
Section
Research articles