## Asymptotic behaviour of positive solutions of $$x'' = t^{\alpha \lambda - 2} x^{1 + \alpha}$$ where $$\alpha = {\lambda}_0$$ and $$\lambda > 0$$.(English)Zbl 1353.34055

Summary: Through analytical expressions, we state the asymptotic behaviour of the positive solutions of the differential equation denoted in the title, depending on the orbit of the two-dimensional autonomous system into which this differential equation is transformed. We treat the case when this autonomous system has an improper node as its critical point.

### MSC:

 34D05 Asymptotic properties of solutions to ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations