A polyharmonic equation on the sphere in the three-dimensional space

We consider a nonhomogeneous polyharmonic equation on the unit sphere in the three-dimensional Euclidean space. Sobolev spherical spaces act as functional classes in which solutions to the spherical polyharmonic equation are sought. It is proved that for a given right-hand side of the equation, which is orthogonal to the identically-one function, the solution to the equation exists in the spherical Sobolev space and is unique there. We establish that for small variations of the right-hand side of the polyharmonic equation under consideration, its solutions change little in the corresponding norm.