Abstract
In the paper, we study uniqueness problems for solutions of a boundary value problem for a polyharmonic equation in the exterior of a compact set and in a half-space under the assumption that the generalized solution of the problem in question admits a finite Dirichlet integral with a weight of the form |x| a . In dependence on the values of the parameter a, we prove uniqueness theorems and also present precise formulas to evaluate the dimension of the space of solutions of this problem in the exterior of a compact set and in a half-space.
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