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

Tsukamoto, Ichiro

Comment. Math. Univ. St. Pauli 65, No. 1, 15-34 (2016).

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

Keywords:

asymptotic behaviour; analytical expression; initial value problem; first-order rational differential equation; two-dimensional autonomous system