On Asymptotic Behaviour of Positive Solutions of x''=-t^(-α/2-2)ｘ^(１+α) in the Superlinear Case

As a continuation work, we consider an initial value problem of the differential equation written in the title.For this, we transform the differential equation into a two dimensional autonomous system which has a centre as its critical point.We prove that this system has three kinds of orbits.Depending on these kinds, we get analytical expressions of the solution of the initial value problem which show its asymptotic behaviour.In the end, we state asymptotic behaviour of all positive solutions.