Geodesic
The biharmonic Neumann problem with double involution
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 16 (2024) no. 3, pp. 18-26

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This paper studies the solvability of a new class of boundary value problems with nonlocal Neumann conditions for a biharmonic equation in a sphere. Non-local conditions are specified in the form of a connection between the values of the desired function at different points of the boundary. In this case, the boundary operator is determined using matrices of involution-type mappings. The theorem of existence the and uniqueness of the solution is proved and the integral representation of the solution to the problem under consideration is found.
Keywords: nonlocal Neumann problem, biharmonic equation, solvability conditions, Green's function. 
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     author = {V. V. Karachik},
     title = {The biharmonic {Neumann} problem with double involution},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {18--26},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2024_16_3_a2/}
}
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V. V. Karachik. The biharmonic Neumann problem with double involution. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 16 (2024) no. 3, pp. 18-26. http://geodesic.mathdoc.fr/item/VYURM_2024_16_3_a2/