A class of first-order nonlinear difference equations of neutral type

Approximative solutions to difference equations of neutral type

“…By Lemma 3.1, any sequence in Geo (λ, k) is a product of a geometric sequence and a periodic sequence. if k > 0, then x ∈ S ⇐⇒ x n+k = λx n for any n ≥ 0, (11) if k < 0, then x ∈ S ⇐⇒ x n+l = qx n for any n ≥ 0.…”

“…By a solution of (E) we mean a sequence x: N(0) → R satisfying (E) for all large n. Asymptotic properties of solutions to neutral equations were investigated in many papers, see, for example, [1][2][3][4][5][6][7][8][9], [11][12][13].…”

Nonoscillatory Solutions to Second-Order Neutral Difference Equations

“…for p = −1 were obtained by Tian et al in [21]. Moreover, for classification of nonoscillatory solutions to equations of the type defined by Equation 1, see [22][23][24][25][26].…”

Asymptotically polynomial solutions to difference equations of neutral type

“…These studies tend in several directions. For example, the papers [3], [15], [17] and [25] are devoted to the classification of solutions. In [8], [9], [11] and [24] where studied solutions with prescribed asymptotic behavior.…”