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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
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