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Asymptotic forms of positive solutions of second-order quasilinear ordinary differential equations with sub-homogeneity. (English) Zbl 0997.34038
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.
Reviewer: P.Smith (Keele)

##### MSC:
 34D05 Asymptotic properties of solutions to ordinary differential equations 34E05 Asymptotic expansions of solutions to ordinary differential equations