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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| Format: | Article |
| Language: | English |
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Wiley
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171283000332 |
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| _version_ | 1832562135673077760 |
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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. |
| format | Article |
| id | doaj-art-dd1dccee103145ae8f61110e9d9973bc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1983-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |
| work_keys_str_mv | AT johnwhooker ahillewintnertypecomparisontheoremforsecondorderdifferenceequations AT johnwhooker hillewintnertypecomparisontheoremforsecondorderdifferenceequations |