Uniqueness of the Adjoint Problem in the Lagrange Sense for a Non-Local Boundary Problem with Complex Parameter

The article is devoted to the problem of finding conjugate boundary conditions for a nonlocal conditional problem for a homogeneous ordinary differential equation of the second order, the coefficients of which depend on a complex parameter. The conjugate boundary conditions known in the literature, associated with arbitrary constants, are investigated, and the issue of eliminating arbitrariness in boundary conditions is considered.