Sturm-Liouville operator with general boundary conditions

Abstract

We classify the general linear boundary conditions involving $u''$, $u'$ and $u$ on the boundary ${a,b}$ so that a Sturm-Liouville operator on $[a,b]$ has a unique self-adjoint extension on a suitable Hilbert space.

Keywords

• Sturm-Liouville operator
• Wentzell boundary conditions
• nonseparated and separated boundary conditions
• symmetric operators.