TRANSFORMATION OF STURM–LIOUVILLE PROBLEMS WITH DECREASING AFFINE BOUNDARY CONDITIONS

• Published in: Proceedings of the Edinburgh Mathematical Society Vol. 47; no. 3; pp. 533 - 552
• Main Authors: Binding, Paul A., Browne, Patrick J., Code, Warren J., Watson, Bruce A.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.10.2004
• Subjects: Darboux transformation; eigenparameter-dependent boundary conditions; Sturm–Liouville; Sturm–Liouville; eigenparameter-dependent boundary conditions; Darboux transformation

We consider Sturm–Liouville boundary-value problems on the interval $[0,1]$ of the form $-y''+qy=\lambda y$ with boundary conditions $y'(0)\sin\alpha=y(0)\cos\alpha$ and $y'(1)=(a\lambda+b)y(1)$, where $a\lt0$. We show that via multiple Crum–Darboux transformations, this boundary...