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 |
| Language: | English |
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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 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |