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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Note on a theorem of Avakumović


Author: J. L. Geluk
Journal: Proc. Amer. Math. Soc. 112 (1991), 429-431
MSC: Primary 34E05; Secondary 26A12
MathSciNet review: 1052570
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Abstract: A short proof is given of a result due to Avakumović. More specifically the asymptotic behavior of the solution $ y\left( x \right) \to 0\left( {x \to \infty } \right)$ of the differential equation $ y'' = \phi \left( x \right){y^\lambda }\left( {\lambda > 1} \right)$ in case $ \phi \left( {tx} \right)/\phi \left( x \right) \to {t^\sigma }\left( {x \to \infty } \right),\sigma > - 2$ is given.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1052570-5
PII: S 0002-9939(1991)1052570-5
Article copyright: © Copyright 1991 American Mathematical Society