Adjoint n-point Boundary Value Problem for the Linear Differential Equation and Green's Function

The n-point problem with linear boundary conditions of general type is studied in this work. We have found the boundary conditions for the adjoint differential operator. The Green's function has been constructed where we have used solutions of the adjoint differential equation and studied its new properties. Through the Green's function and saltus of its derivatives, we have solved the nonhomogeneous n-point boundary value problem for the linear differential equation with variable coefficients.