Open AccessAn inverse problem for the second-order integro-differential pencil
Author(s) -
Natalia P. Bondarenko
Publication year - 2019
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.50.2019.3348
Subject(s) - mathematics , pencil (optics) , uniqueness , boundary value problem , inverse , eigenvalues and eigenvectors , constructive , inverse problem , polynomial , mathematical analysis , geometry , mechanical engineering , physics , process (computing) , quantum mechanics , computer science , engineering , operating system
We consider the second-order (Sturm-Liouville) integro-differential pencil with polynomial dependence on the spectral parameter in a boundary condition. The inverse problem is solved, which consists in reconstruction of the convolution kernel and one of the polynomials in the boundary condition by using the eigenvalues and the two other polynomials. We prove uniqueness of solution, develop a constructive algorithm for solving the inverse problem, and obtain necessary and sufficient conditions for its solvability.