Hill's equation revisited (Q1076877)

This paper has to do with Hill's equation written in the form \((1)\quad y''+(a+b\sin x)y=0,\) where a and b are real constants \((a<0)\). A sequence of regions \(R_ n\) \((R_ n\supset R_{n-1})\) of the ab-plane is determined with the property that if the point \((a,b)\in R_ n\), solutions of (1) are oscillatory.