## On asymptotic behaviour of positive solutions of $$x^{\prime \prime}\, =\, -t^{\alpha \lambda -2}x^{1+\alpha}$$ with $$\alpha > \lambda_0 , -1<\lambda < 0$$.(English)Zbl 1300.34127

Summary: We consider an initial value problem of the differential equation denoted in the title, and show the domain of its positive solution and the analytical expressions of this valid in the neighbourhoods of the ends of the domain. This is done for all initial conditions.

### MSC:

 34D05 Asymptotic properties of solutions to ordinary differential equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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