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.
Author Biography
Valeriy Valentinovich Karachik, South Ural State University, Chelyabinsk
Dr. Sc. (Physics and Mathematics), Professor, Mathematical Analysis and Methods of Teaching Mathematics Department, Senior Staff Scientist
