Abstract
In this paper, the inverse Sturm–Liouville problem with distribution potential and with polynomials of the spectral parameter in one of the boundary conditions is considered. We for the first time prove local solvability and stability of this inverse problem in the general non-self-adjoint case, taking possible splitting of multiple eigenvalues into account. The proof is based on the reduction of the non-linear inverse problem to a linear equation in the Banach space of continuous functions on some circular contour. Moreover, we introduce the generalized Cauchy data, which will be useful for investigation of partial inverse Sturm–Liouville problems with polynomials in the boundary conditions. Local solvability and stability of recovering the potential and the polynomials from the generalized Cauchy data are obtained. Thus, the results of this paper include the first existence theorems for solution of the inverse Sturm–Liouville problems with polynomial dependence on the spectral parameter in the boundary conditions in the case of multiple eigenvalues. In addition, our stability results can be used for justification of numerical methods.
Funding source: Russian Science Foundation
Award Identifier / Grant number: 21-71-10001
Funding statement: This work was supported by Grant 21-71-10001 of the Russian Science Foundation.
References
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© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- An inverse problem for non-selfadjoint Dirac operator with transmission conditions at finite interior points
- Inverse Sturm–Liouville problem with polynomials in the boundary condition and multiple eigenvalues
- Blow-up of solutions to some classes of ill-posed operator equations and a growth quantification result
- On an inverse problem with high-order overdetermination conditions
- Two regularization methods for identifying the source term of Caputo–Hadamard type time fractional diffusion-wave equation
- Integrating the probe and singular sources methods: III. Mixed obstacle case
- Stability estimate and the Tikhonov regularization method for the Kuramoto–Sivashinsky equation backward in time
- Continuation of solutions of elliptic systems from discrete sets with application to geometry of surfaces
Artikel in diesem Heft
- Frontmatter
- An inverse problem for non-selfadjoint Dirac operator with transmission conditions at finite interior points
- Inverse Sturm–Liouville problem with polynomials in the boundary condition and multiple eigenvalues
- Blow-up of solutions to some classes of ill-posed operator equations and a growth quantification result
- On an inverse problem with high-order overdetermination conditions
- Two regularization methods for identifying the source term of Caputo–Hadamard type time fractional diffusion-wave equation
- Integrating the probe and singular sources methods: III. Mixed obstacle case
- Stability estimate and the Tikhonov regularization method for the Kuramoto–Sivashinsky equation backward in time
- Continuation of solutions of elliptic systems from discrete sets with application to geometry of surfaces