TY - JOUR
A2 - Braverman, Elena
AU - Berezansky, L.
AU - Diblík, J.
AU - Růžičková, M.
AU - Šutá, Z.
PY - 2011
DA - 2011/06/30
TI - Asymptotic Convergence of the Solutions of a Discrete Equation with Two Delays in the Critical Case
SP - 709427
VL - 2011
AB - A discrete equation Δy(n)=β(n)[y(n−j)−y(n−k)] with two integer delays k and j, k>j≥0 is considered for n→∞. We assume β:ℤn0−k∞→(0,∞), where ℤn0∞={n0,n0+1,…}, n0∈ℕ and n∈ℤn0∞. Criteria for the existence of strictly monotone and asymptotically convergent solutions for n→∞ are presented in terms of inequalities for the function β. Results are sharp in the sensethat the criteria are valid even for some functions β with a behavior near the so-called critical value, defined by the constant (k−j)−1. Among others, it is proved that, for the asymptotic convergence of all solutions, the existence of a strictly monotone and asymptotically convergent solution is sufficient.
SN - 1085-3375
UR - https://doi.org/10.1155/2011/709427
DO - 10.1155/2011/709427
JF - Abstract and Applied Analysis
PB - Hindawi Publishing Corporation
KW -
ER -