Nonlocal Multipoint Problem for Partial Differential Equations of Even Order with Constant Coefficients

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

Baranetskij

Демків

Kalenyuk

2023

J Math Sci

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A nonlocal problem with multipoint perturbations of strongly regular Birkhoff boundary conditions for an even-order differential operator

Baranetskij¹,

Демків²,

Kalenyuk³

2020

Mat. Met. Fiz. Mekh. Polya

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Nonlocal Multipoint Problem for Partial Differential Equations of Even Order with Constant Coefficients

Cited by 2 publications

References 13 publications

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

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

A nonlocal problem with multipoint perturbations of strongly regular Birkhoff boundary conditions for an even-order differential operator

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