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

Abstract

In this paper, we, for the first time, prove the local solvability and stability of an inverse spectral problem for higher-order (n>3) differential operators with distribution coefficients. The inverse problem consists of the recovery of differential equation coefficients from (n−1) spectra and the corresponding weight numbers. The proof method is constructive. It is based on the reduction of the nonlinear inverse problem to a linear equation in the Banach space of bounded infinite sequences. We prove that, under a small perturbation of the spectral data, the main equation remains uniquely solvable. Furthermore, we estimate the differences of the coefficients in the corresponding functional spaces.

Keywords

• inverse spectral problem
• higher-order differential operators
• distribution coefficients
• local solvability
• stability