NEUMANN BOUNDARY CONDITION FOR A NONLOCAL BIHARMONIC EQUATION

The solvability conditions for a class of boundary value problems nonlocal biharmonic equation in the unit ball with Neumann on are studied. nonlocality is generated by some orthogonal matrix. presence and uniqueness solution to proposed condition examined, an integral representation Dirichlet problem terms Green's function obtained. First, auxiliary statements established: given, this written, values integrals functions perturbed matrix found. Then theorem proved. written using regular equation. An example solving simple given. Next, we formulate necessary sufficient main proved based two lemmas, help which it possible transform simpler form. presented through problem.