On the Solvability Conditions for the Neumann Boundary Value Problem

Abstract

In previous work of the first author, a solvability condition of the Neumann boundary value problem for the polyharmonic equation in the unit ball was obtained. This condition has a form of equality to zero of some integral of a linear combination of the boundary functions. In the present paper coefficients of that linear combination are explicitly obtained. In the investigation an arithmetical triangle is arisen. For elements of this triangle a recurrence relation similar to binomial coefficients is derived. It managed to get an explicit solution of the recurrence relation obtained.