Sobolev-Trenogin Principle in Construction of the Boundary Value Problem Adjoint to the Linear Multipoint Problem

The research has been done in two directions. In a linear case, the adjoint boundary problem have been built. We have managed to do it in a classical continuous case without resort to such terms of functional analysis as an adjoint space, adjoint operator, etc. In a non-linear case, we have considered the problem with a small parameter and discussed an issue of applicability of some aspects of a theory of bifurcation of the nonlinear equations' solutions (Trenogin et al., 1991). We have built a boundary problem adjoint to the linear multipoint problem. We have studied unicity of its linear and adjoint differential operators with multipoint boundary conditions and generalized it for the m-point problem.