Article

    Ufa Mathematical Journal
    Volume 3, Number 2, pp. 27-32

    About the stability of basis property of one type of problems on the eigenvalues with nonlocal perturbation of boundary conditions


    Imanbaev N.S., Sadybekov M.A.

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    The article presents a spectral problem for a multiple differentiation operator with an integral perturbation of boundary conditions of one type which are regular, but not strongly regular. The unperturbed problem has asymptotically simple spectrum, and its system of normalized eigenfunctions creates Riesz basis. We construct the characteristic determinant of the spectral problem with an integral perturbation of boundary conditions. The perturbed problem can have any finite number of multiple eigenvalues. Therefore, its root subspace consists of its eigen and (maybe) adjoint functions. It is shown that the Riesz basis property of system of eigen and adjoint functions is stable with respect to integral perturbations of the boundary condition.