Identification of boundary conditions of a differential operator

Abstract

This pap er consists of three parts. To achieve uniqueness of the solution of the B max u = h
indicated inhomogeneous equation, it is necessary to narrow the domain of definition of the
maximum op erator. The narrowing usually o ccurs due to b oundary conditions. Thus, a class of
correct restrictions of the maximum op erator arises. In the second part of the article, we give
the pro of of Theorem 1 and the justification of the pro cedure for recovering b oundary functions
{ σ 2 ( t ) , . . . , σ n ( t ) } . In the third part of the article, we separately consider the case of reconstructing
two-point boundary value problems from a finite set of eigenvalues and give illustrative numerical
examples of approximate calculations of the coefficients of the boundary conditions. Note that the
problem of recovering boundary functions { σ 2 ( t ) , . . . , σ n ( t ) } from the procedure we have proposed,
the linear problem. This fact is not obvious if the initial set of boundary functions is restored { σ j k } .