TY - JOUR
T1 - Necessary and sufficient conditions for solvability of the Hartman-Wintner problem for difference equations
AU - Chernyavskaya, N. A.
AU - Shuster, L. A.
PY - 2008/12
Y1 - 2008/12
N2 - The equation Δ(rn-1Δyn-1) = (q n + σn)yn, n≥0 (1) is viewed as a perturbation of the equation Δ(rn-1Δzn-1) = qnzn, n≥0 (2) which does not oscillate at infinity. The sequences {rn}n=0∞, {qn} n=0∞ are assumed real, rn>0 for all n ≥ 0, the sequences {σn}n=0∞ may be complex-valued. We study the Hartman-Wintner problem on asymptotic 'integration' of (1) for large n in terms of solutions of (2) and the perturbation {σn}n=0∞.
AB - The equation Δ(rn-1Δyn-1) = (q n + σn)yn, n≥0 (1) is viewed as a perturbation of the equation Δ(rn-1Δzn-1) = qnzn, n≥0 (2) which does not oscillate at infinity. The sequences {rn}n=0∞, {qn} n=0∞ are assumed real, rn>0 for all n ≥ 0, the sequences {σn}n=0∞ may be complex-valued. We study the Hartman-Wintner problem on asymptotic 'integration' of (1) for large n in terms of solutions of (2) and the perturbation {σn}n=0∞.
KW - FSS
KW - Hartman-Wintner
KW - Necessary
KW - Sufficient
UR - http://www.scopus.com/inward/record.url?scp=54349100269&partnerID=8YFLogxK
U2 - 10.1080/10236190701827911
DO - 10.1080/10236190701827911
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AN - SCOPUS:54349100269
SN - 1023-6198
VL - 14
SP - 1215
EP - 1254
JO - Journal of Difference Equations and Applications
JF - Journal of Difference Equations and Applications
IS - 12
ER -