2023/03/23 by Natalia P. Bondarenko, Bondarenko, Natalia P. · 1 citation
Computer Science · Mathematics · #34A55 34B09 34B05 34E05 46F10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2303.13124
openalex publication_date 2023/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of the differential expression coefficients from the spectral data of two boundary value problems with separated boundary conditions. For this inverse problem, we solve the most fundamental question of the inverse spectral theory about the necessary and sufficient conditions of solvability. In addition, we prove the local solvability and stability of the inverse problem. Furthermore, we obtain very simple sufficient conditions of solvability in the self-adjoint case. The main results are proved by a constructive method that reduces the nonlinear inverse problem to a linear equation in the Banach space of bounded infinite sequences. In the future, our results can be generalized to various classes of higher-order differential operators with integrable or distribution coefficients.