Weak and strong stability of the inverse Sturm‐Liouville problem

Abstract

In this work, we study the stability of the inverse Sturm‐Liouville problem with the Neumann boundary condition at the left ending point and the Robin boundary condition at the right ending point. We estimate the difference of two potentials in the sense of weakness and ‐norm, in terms of the difference of two spectra. Since the Neumann boundary condition may become the Robin boundary condition after small perturbation of the spectra, our stability results also include this situation.

Local Solvability and Stability of an Inverse Spectral Problem for Higher-Order Differential Operators

“…Then, using ( 27), ( 28), (46), and the above estimates for G(ν) (l,k,ε),(l 0 ,k 0 ,ε 0 ) (x), we obtain…”

“…In this paper, we focus on the local solvability and stability of the inverse problem. These aspects for the Sturm-Liouville operators were studied in [8][9][10]12,15,16,18,[37][38][39][40][41][42][43][44][45][46] and many other papers. Local solvability has a fundamental significance in inverse problem theory, especially for such problems, for which global solvability theorems are absent or contain hard-to-verify conditions.…”

Local solvability and stability for the inverse Sturm‐Liouville problem with polynomials in the boundary conditions

“…Local solvability and stability of inverse problems for various classes of the Sturm-Liouville operators were investigated in [3,23,[38][39][40][41][42][43][44][45] and other studies. Local solvability is an important property of inverse problems, especially in the cases when it is difficult to prove the global solvability.…”