TRANSFORMATION OF STURM–LIOUVILLE PROBLEMS WITH DECREASING AFFINE BOUNDARY CONDITIONS - Binding, Paul A.; Browne, Patrick J.; Code, Warren J.; Watson, Bruce A. (Proceedings of the Edinburgh Mathematical Society, 2004)
We consider Sturm–Liouville boundary-value problems on the interval $[0,1]$ of the form $-y''+qy=λ y$ with boundary conditions $y'(0)\sinα=y(0)\cosα$ and $y'(1)=(aλ+b)y(1)$, where $a\lt0$. We show that via multiple Crum–Darboux transformations, this boundary-value problem can be transformed ‘almost’ isospectrally to a boundary-value problem of the same form, but with the boundary condition at $x=1$ replaced by $y'(1)\sinβ=y(1)\cosβ$, for some $β$. AMS 2000 Mathematics subject classification: Primary 34B07; 47E05; 34L05