Necessary and sufficient conditions for solvability of the Hartman-Wintner problem for difference equations

N. A. Chernyavskaya; L. A. Shuster

doi:10.1080/10236190701827911

Necessary and sufficient conditions for solvability of the Hartman-Wintner problem for difference equations

N. A. Chernyavskaya, L. A. Shuster

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The equation Δ(r_n-1Δy_n-1) = (q _n + σ_n)y_n, n≥0 (1) is viewed as a perturbation of the equation Δ(r_n-1Δz_n-1) = q_nz_n, n≥0 (2) which does not oscillate at infinity. The sequences {r_n}_n=0^∞, {q_n} _n=0^∞ are assumed real, r_n>0 for all n ≥ 0, the sequences {σ_n}_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 {σ_n}_n=0^∞.

Original language	English
Pages (from-to)	1215-1254
Number of pages	40
Journal	Journal of Difference Equations and Applications
Volume	14
Issue number	12
DOIs	https://doi.org/10.1080/10236190701827911
State	Published - 1 Dec 2008

Keywords

FSS
Hartman-Wintner
Necessary
Sufficient

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1080/10236190701827911

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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∞.",

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AU - Chernyavskaya, N. A.

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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

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Necessary and sufficient conditions for solvability of the Hartman-Wintner problem for difference equations

Abstract

Keywords

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