On the solvability of a Dirichlet-type problem for a nonlocal polyharmonic equation

Ainur Shalkhar

2026

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DOI 10.70474/e9jn1113
Data confidence 70 medium
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Abstract

The subject of the study is the solvability of one class of boundary value problems for a nonlocal polyharmonic equation. The nonlocal polyharmonic operator and boundary operators are generated using some orthogonal matrices. The existence and uniqueness of a solution to the Dirichlet-type problem are investigated, and the Green’s function is constructed. Furthermore, the corresponding spectral problem is studied. The eigenfunctions and eigenvalues of the problem under consideration are found explicitly. The theorem on the completeness of systems of eigenfunctions in the space L₂ is proved.