Abstract
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∞.
Original language | English |
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Pages (from-to) | 1215-1254 |
Number of pages | 40 |
Journal | Journal of Difference Equations and Applications |
Volume | 14 |
Issue number | 12 |
DOIs | |
State | Published - 1 Dec 2008 |
Keywords
- FSS
- Hartman-Wintner
- Necessary
- Sufficient
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Applied Mathematics