A Hille-Wintner type comparison theorem for second order difference equations

For the linear difference equation Δ(cn−1Δxn−1)+anxn=0   with   cn>0, a non-oscillation comparison theorem given in terms of the coefficients cn and the series ∑n=k∞an, has been proved.

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Main Author: John W. Hooker
Format: Article
Language:English
Published: Wiley 1983-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171283000332
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author John W. Hooker
author_facet John W. Hooker
author_sort John W. Hooker
collection DOAJ
description For the linear difference equation Δ(cn−1Δxn−1)+anxn=0   with   cn>0, a non-oscillation comparison theorem given in terms of the coefficients cn and the series ∑n=k∞an, has been proved.
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1687-0425
language English
publishDate 1983-01-01
publisher Wiley
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-dd1dccee103145ae8f61110e9d9973bc2025-02-03T01:23:20ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251983-01-016238739310.1155/S0161171283000332A Hille-Wintner type comparison theorem for second order difference equationsJohn W. Hooker0Department of Mathematics, Southern Illinois University, Carbondale 62901, Illinois, USAFor the linear difference equation Δ(cn−1Δxn−1)+anxn=0   with   cn>0, a non-oscillation comparison theorem given in terms of the coefficients cn and the series ∑n=k∞an, has been proved.http://dx.doi.org/10.1155/S0161171283000332difference equationsoscillatory and non-oscillatory solutions comparison theoremsRiccati transformation.
spellingShingle John W. Hooker
A Hille-Wintner type comparison theorem for second order difference equations
International Journal of Mathematics and Mathematical Sciences
difference equations
oscillatory and non-oscillatory solutions comparison theorems
Riccati transformation.
title A Hille-Wintner type comparison theorem for second order difference equations
title_full A Hille-Wintner type comparison theorem for second order difference equations
title_fullStr A Hille-Wintner type comparison theorem for second order difference equations
title_full_unstemmed A Hille-Wintner type comparison theorem for second order difference equations
title_short A Hille-Wintner type comparison theorem for second order difference equations
title_sort hille wintner type comparison theorem for second order difference equations
topic difference equations
oscillatory and non-oscillatory solutions comparison theorems
Riccati transformation.
url http://dx.doi.org/10.1155/S0161171283000332
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