Asymptotic behavior of higher-order neutral difference equations with general arguments - Chatzarakis, G. E.; Khatibzadeh, H.; Miliaras, G. N.; Stavroulakis, I. P. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
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.