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

Kazbek A. Khasseinov

Abstract


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.

Full Text: PDF DOI: 10.5539/jmr.v5n1p41

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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