A nonlocal problem with multipoint perturbations of periodic conditions for differential operator equations of even order

Baranetskyi Yaroslav Omelyanovych

doi:https://doi.org/10.31861/bmj2018.03.017

Baranetskyi Yaroslav Omelyanovych ¹

¹ Department of Computational Mathematics and Programming., Lviv Polytechnic National University, Lviv, 79013, Ukraine

DOI: https://doi.org/10.31861/bmj2018.03.017

Keywords: problem with multipoint condition, periodic condition, іnvariant subspaces, perturbed conditions

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Abstract

For a differential equation whose coefficients are self-adjoint operators, a problem with multipoint conditions that contain periodic conditions is investigated. It is established that the operator of the problem has two invariant subspaces generated by the involution operator and two subsystems of the system of eigenfunctions, which are orthonormal bases in each of the subspaces. For an operator-differential equation of even order, a problem with non-self-adjoint multipoint boundary conditions, which are perturbations of periodic conditions, was studied. The cases when the perturbed conditions are regular but not strongly regular behind Birkhoff are investigated. The eigenvalues and elements of the system of root functions $V$ of the operator of the problem, which is complete and contains an infinite number of associated functions, are defined. Sufficient conditions are obtained under which the system $V$ is the Riesz base. The conditions of existence and uniqueness of the solution of the problem with homogeneous boundary conditions, constructed in the form of expansion in a series in the system $V$ , are established.

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ACS Style: Baranetskyi, Y.O. A nonlocal problem with multipoint perturbations of periodic conditions for differential operator equations of even order. Bukovinian Mathematical Journal. 2019, 6 https://doi.org/ https://doi.org/10.31861/bmj2018.03.017
AMA Style: Baranetskyi YO. A nonlocal problem with multipoint perturbations of periodic conditions for differential operator equations of even order. Bukovinian Mathematical Journal. 2019; 6(3-4). https://doi.org/ https://doi.org/10.31861/bmj2018.03.017
Chicago/Turabian Style: Yaroslav Omelyanovych Baranetskyi. 2019. "A nonlocal problem with multipoint perturbations of periodic conditions for differential operator equations of even order". Bukovinian Mathematical Journal. 6 no. 3-4. https://doi.org/ https://doi.org/10.31861/bmj2018.03.017

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