On solutions of the Lagerstrom equation. (English) Zbl 0674.34024

Vrdoljak, Božo

Arch. Math., Brno 24, No. 3, 111-122 (1988).

The Lagerstrom equation is \(y''+(2/t+y)y'=0\) where \(t\in (a,b)\), \(-\infty \leq a<b<0\) or \(0<a<b\leq +\infty\). The paper deals with the behaviour of certain classes of Cauchy’s solutions of the Lagerstrom equation. It considers the behaviour of solutions in the neighborhood of an arbitrary or an integral curve on a finite or infinite interval. The sufficient conditions which garantee certain behavior of some classes of Cauchy’s solutions are given. The results obtained refer also to an approximation and asymptotic behaviour of solutions.

Reviewer: G.Osipenko

MSC:

34C05

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations

Keywords:

Cauchy’s solutions; Lagerstrom equation