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Nonlocal Problem with Multipoint Perturbations of the Birkhoff Strongly Regular Boundary Conditions for an Even-Order Differential Operator

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We study spectral properties of a nonself-adjoint problem for a (2n) th order operator of differentiation with nonlocal conditions representing multipoint perturbations of the Birkhoff strongly regular self-adjoint conditions. We establish sufficient conditions under which the system of eigenfunctions is complete and, under certain additional assumptions, forms a Riesz basis. We construct a set of transformation operators, each element of which maps the system of eigenfunctions of the unperturbed problem into the system of eigenfunctions of a certain isospectral problem. The cases of problems with Birkhoff regular and irregular two-point perturbations are analyzed. Finally, we establish conditions for the existence and uniqueness of the solution of the studied problem.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, Lviv, Ukraine

    Ya. О. Baranetskij, І. І. Demkiv & P. І. Kalenyuk

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  1. Ya. О. Baranetskij
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  2. І. І. Demkiv
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  3. P. І. Kalenyuk
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Correspondence to Ya. О. Baranetskij.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 1, pp. 21–36, January–March, 2020.

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Baranetskij, Y.О., Demkiv, І.І. & Kalenyuk, P.І. Nonlocal Problem with Multipoint Perturbations of the Birkhoff Strongly Regular Boundary Conditions for an Even-Order Differential Operator. J Math Sci 270, 19–38 (2023). https://doi.org/10.1007/s10958-023-06330-3

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