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Proceedings of the American Mathematical Society

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Asymptotic behavior of the solutions of the second order difference equation


Authors: Andrzej Drozdowicz and Jerzy Popenda
Journal: Proc. Amer. Math. Soc. 99 (1987), 135-140
MSC: Primary 39A12; Secondary 34K15
DOI: https://doi.org/10.1090/S0002-9939-1987-0866443-0
MathSciNet review: 866443
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Abstract: The second order difference equation (E)

$\displaystyle {\Delta ^2}{x_n} + {p_n}f({x_n}) = 0$

is considered. The results give a necessary and sufficient condition for some solution of (E) to have asymptotic behavior $ {x_n} \sim C =$   const. as $ n$ approaches infinity.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0866443-0
Keywords: Difference equation, asymptotic behavior
Article copyright: © Copyright 1987 American Mathematical Society