Asymptotic properties of the solutions of a differential equation appearing in QCD

Abstract

We establish the asymptotic behaviour of the ratio $h^\prime(0)/h(0)$ for $λ\rightarrow\infty$, where $h(r)$ is a solution, vanishing at infinity, of the differential equation $h^{\prime\prime}(r) = iλω(r) h(r)$ on the domain $0 \leq r <\infty$ and $ω(r) = (1-\sqrt{r} K_1(\sqrt{r}))/r$. Some results are valid for more general $ω$&#39;s.