Criteria for the uniqueness of a solution for some differential-operator equation
DOI:
https://doi.org/10.70474/2pmhkg48Keywords:
complete orthogonal systems, non-degenerate boundary conditions, operator eigenvalues, operator spectrum, Sturm-Liouville equation, symmetric operator part, uniqueness of solutionAbstract
Abstract. In this article, the symmetric operator L; corresponding to the boundary value problem is represented as the difference of two commuting operators A and B: The uniqueness of the solution is guaranteed if the spectra of the operators A and B do not intersect and the domain of the operator B is given by non-degenerate boundary conditions. In contrast to the existing papers, the criterion for the uniqueness of the boundary value problem formulated in this paper is satisfied even when the system of root functions of the operator B does not form a basis in the corresponding space. At the same time, only the closedness of the linear operator A is required.
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