Asymptotic behavior for non-oscillatory solutions of difference equations with several delays in the neutral term

Abstract

In this paper, we first consider difference equations with several delays in the neutral term of the form ⎛study various cases of coefficients in the neutral term and obtain the asymptotic behavior for non-oscillatory solution of ( * ) under some hypotheses. Moreover, we consider reaction-diffusion difference equations with several delays in the neutral term of the formr j u n−ρ j ,m ⎞ ⎠ + q n,m u n−τ,m = a 2 2 2 u n+1,m−1 for (n, m) ∈ Z + (0) × , study various cases of coefficients in the neutral term and obtain the asymptotic behavior for non-oscillatory solution under some hypotheses.

Asymptotic and oscillatory behavior of certain second order neutral delay difference equations

“…Next, we claim the map T is continuous. Assume that x (m) is a sequence in B such that lim Since B is closed and x ∈ B, from equations (11), (14) and conditions (C1),(C2),(C3), we obtain…”

“…The author [15] has considered the cases of p n = 0 and q n ≡ 0, the author [12] has considered the cases of both p n ≡ 0 and q n ≡ 0. Few authors [14,16] have studied the both positive and negative neutral terms in the first order difference equations.…”