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

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For a partial differential equation of even order with constant coefficients, in a bounded domain G, we study a problem with boundary conditions in the form of multipoint perturbations of the Neumann conditions by using the Fourier method. The eigenvalues and eigenfunctions of the operator L of the multipoint problem are determined. We establish the conditions of completeness of the system of eigenfunctions V(L) of the operator L in the space L2 (G). In the case of elliptic equation, we establish the conditions under which the system V(L) is a Riesz basis in the space L2 (G). We construct the solution of an inhomogeneous problem with homogeneous multipoint conditions in the form of a Fourier series with respect to the system of eigenfunctions and establish conditions for its existence and uniqueness.

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Authors and Affiliations

  1. Lviv Polytechnic National University, Lviv, Ukraine

    Ya. О. Baranetskij & P. І. Kalenyuk

  2. V. Stefanyk Pre-Carpathian National University, Ivano-Frankivs’k, Ukraine

    М. І. Kopach

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

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 61, No. 1, pp. 11–30, January–March, 2018.

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Baranetskij, Y.О., Kalenyuk, P.І. & Kopach, М.І. Nonlocal Multipoint Problem for Partial Differential Equations of Even Order with Constant Coefficients. J Math Sci 249, 307–332 (2020). https://doi.org/10.1007/s10958-020-04945-4

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