Existence of logarithmic-type solutions to the Kapila-Kassoy problem in dimensions 3 through 9 (Q1105091)

The authors investigate the differential equation \[ y''+(\frac{n-1}{x}- \frac{x}{2})y'+e^ y-1=0,\quad 0<x<\infty \] and denote by y(x,\(\alpha)\) the solution of it satisfying \(y(0)=\alpha \in {\mathbb{R}}\) and \(y'(0)=0\). They prove that for each integer \(n\in (2,10)\) there is an unbounded sequence of positive numbers \(\{\bar\alpha_ m(n)\}^{\infty}_{m=1}\) such that the solutions \(y(x,{\bar\alpha}_ m)\) satisfy the limit condition: \(\lim_{x\to \infty}[1+(1/2)xy'(x)]=0.\)