Existence theorem for the difference equation Yn+1−2Yn+Yn−1=h2f(yn)
For the difference equation (Yn+1−2Yn+Yn−1)h2=f(Yn) sufficient conditions are shown such that for a given Y0 there is either a unique value of Y1 for which the sequence Yn strictly monotonically approaches a constant as n approaches infinity or a continuum interval of such values. It has been shown...
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| Format: | Article |
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Hindawi Limited
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171280000051 |
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doaj-1f6c8328dc5a464cb3b509cff8e94fb22020-11-24T23:50:05ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-0131697710.1155/S0161171280000051Existence theorem for the difference equation Yn+1−2Yn+Yn−1=h2f(yn)F. Weil0Department of Physics-Mathematics, Université de Moncton, Moncton, N. B., CanadaFor the difference equation (Yn+1−2Yn+Yn−1)h2=f(Yn) sufficient conditions are shown such that for a given Y0 there is either a unique value of Y1 for which the sequence Yn strictly monotonically approaches a constant as n approaches infinity or a continuum interval of such values. It has been shown previously that the first alternative is related to the existence of a Peierls barrier energy in the dislocation model of Frenkel and Kontorova.http://dx.doi.org/10.1155/S0161171280000051existence theoremdifference equations. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
F. Weil |
| spellingShingle |
F. Weil Existence theorem for the difference equation Yn+1−2Yn+Yn−1=h2f(yn) International Journal of Mathematics and Mathematical Sciences existence theorem difference equations. |
| author_facet |
F. Weil |
| author_sort |
F. Weil |
| title |
Existence theorem for the difference equation Yn+1−2Yn+Yn−1=h2f(yn) |
| title_short |
Existence theorem for the difference equation Yn+1−2Yn+Yn−1=h2f(yn) |
| title_full |
Existence theorem for the difference equation Yn+1−2Yn+Yn−1=h2f(yn) |
| title_fullStr |
Existence theorem for the difference equation Yn+1−2Yn+Yn−1=h2f(yn) |
| title_full_unstemmed |
Existence theorem for the difference equation Yn+1−2Yn+Yn−1=h2f(yn) |
| title_sort |
existence theorem for the difference equation yn+1−2yn+yn−1=h2f(yn) |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1980-01-01 |
| description |
For the difference equation (Yn+1−2Yn+Yn−1)h2=f(Yn) sufficient conditions are shown such that for a given Y0 there is either a unique value of Y1 for which the sequence Yn strictly monotonically approaches a constant as n approaches infinity or a continuum interval of such values. It has been shown previously that the first alternative is related to the existence of a Peierls barrier energy in the dislocation model of Frenkel and Kontorova. |
| topic |
existence theorem difference equations. |
| url |
http://dx.doi.org/10.1155/S0161171280000051 |
| work_keys_str_mv |
AT fweil existencetheoremforthedifferenceequationyn12ynyn1h2fyn |
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1725480145981014016 |