Note on a theorem of Avakumović

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.