|
|||||
|
|
Solvability and stability of the inverse Sturm–Liouville problem with analytical functions in the boundary condition |
|
| Authors: | Natalia P Bondarenko |
| Institution: | Department of Applied Mathematics and Physics, Samara National Research University, Samara, Russia |
| Abstract: | The paper deals with the Sturm–Liouville eigenvalue problem with the Dirichlet boundary condition at one end of the interval and with the boundary condition containing entire functions of the spectral parameter at the other end. We study the inverse problem, which consists in recovering the potential from a part of the spectrum. This inverse problem generalizes partial inverse problems on finite intervals and on graphs and also the inverse transmission eigenvalue problem. We obtain sufficient conditions for global solvability of the studied inverse problem, which prove its local solvability and stability. In addition, application of our main results to the partial inverse Sturm–Liouville problem on the star-shaped graph is provided. |
| Keywords: | analytical dependence on the spectral parameter global solvability inverse problems involving ordinary differential equations linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter local solvability Sturm–Liouville operator |