Hokkaido Mathematical Journal

TSUKAMOTO Ichiro,

On solutions of $x''=t^{\alpha\lambda-2}x^{1+\alpha}$ where $\alpha>0$ and $\lambda=0,-1$.

Hokkaido Mathematical Journal, 35 (2006) pp.41-60

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Abstract

Here we investigate asymptotic behavior of positive solutions of an initial value problem of the second order nonlinear differential equation written in the title. This is done from obtaining analytical expressions of the solution valid in the neighborhoods of both end points of its domain.

MSC(Primary)34A12
MSC(Secondary)34A34
Uncontrolled Keywordsasymptotic behavior, an initial value problem, a two dimensional autonomous system, the Briot-Bouquet differential equation