Direct and inverse Robin-Regge problems. (English) Zbl 1386.34036
Summary: The Sturm-Liouville equation is considered on a bounded interval with a Robin boundary condition at the left end and a generalized Regge condition at the right end. Properties of the spectrum of this problem are derived, including the location of the spectrum in the lower half-plane and the asymptotic distribution of the eigenvalues. The inverse problem is solved, given one spectrum or parts of two spectra.
MSC:
| 34B09 | Boundary eigenvalue problems for ordinary differential equations |
| 34B07 | Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter |
| 34B24 | Sturm-Liouville theory |
| 34L20 | Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators |
| 34A55 | Inverse problems involving ordinary differential equations |
