Inverse problem for Fredholm integro-differential equation with final redefinition conditions at the end of the interval

Abstract

The questions of solvability and construction of solutions of an inverse problem for second-order Fredholm integro-differential equation with degenerate kernel, final conditions at the end of the interval, two parameters, and two redefinition data are considered. The sets of regular parameter values are determined and the corresponding solutions are constructed. The specific features of the inverse problem are studied. Criteria for the unique solvability of the posed inverse problem are established. KEYWORDS integro-differential equation, degenerate kernel, final conditions at the end of a segment, parameters, redefinition data, solvability.