Existence theorem for the difference equation Y n + 1 − 2 Y n + Y n − 1 = h 2 f ( y n )

F. Weil

International Journal of Mathematics and Mathematical Sciences, 1980, vol. 3, 1-9

Abstract:

For the difference equation ( Y n + 1 − 2 Y n + Y n − 1 ) h 2 = f ( Y n ) sufficient conditions are shown such that for a given Y 0 there is either a unique value of Y 1 for which the sequence Y n 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.

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:198414

DOI: 10.1155/S0161171280000051

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