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Zbl 0997.34038
Kamo, Ken-ichi; Usami, Hiroyuki
Asymptotic forms of positive solutions of second-order quasilinear ordinary differential equations with sub-homogeneity.
(English)
[J] Hiroshima Math. J. 31, No.1, 35-49 (2001). ISSN 0018-2079

The authors investigate the asymptotic behaviour of positive solutions to the quasilinear ordinary differential equation $$(|u'|^{\alpha-1} u')'= p(t)|u|^{\lambda- 1}u,$$ subject to the general conditions: (i) $\alpha$ and $\lambda$ are positive constants which satisfy $0< \lambda<\alpha$; (ii) $p: [t_0,\infty)\to (0,\infty)$ is a continuous function such that $p(t)\sim t^\alpha$ as $t\to\infty$. The case $\alpha= 1$ is the well-known Emden-Fowler equation. The uniqueness of positive decaying solutions is also proved.
[P.Smith (Keele)]
MSC 2000:
*34D05 Asymptotic stability of ODE
34E05 Asymptotic expansions (ODE)

Keywords: quasilinear equation; asymptotic forms; positive solutions; Emden-Fowler equation

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