Abstract
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.
Highlights
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
Multipoint Problem have been studied least of all because the interim points included into the boundary conditions cause a range of such serious hardships as breach of smoothness of the Green’s function, absence of the adjoint boundary value Problem, etc
Summary
Multipoint Problem have been studied least of all because the interim points included into the boundary conditions cause a range of such serious hardships as breach of smoothness of the Green’s function, absence of the adjoint boundary value Problem, etc. Redefined multipoint Problem where boundary conditions in the intermediate nodes are “unnecessary”, important in the application context, have been turned out to be poorly studied. These tasks directly relate to the theory of spline (Coddington & Levinson, 1955; Yerugin, 1974; Pokornyi, 1980; Householder, 1956). Construction of the Green’s function for the multipoint Problem with general type boundary conditions and research of its properties are still topical (Kiguradze, 1987; Klokov, 1967; Maksimov & Rakhmatullina, 1977; Liu, 2011; Peterson, 1979; Jackson, 1977)
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