Mixed biharmonic Dirichlet–Neumann problem in exterior domains

We study the unique solvability of the mixed Dirichlet–Neumann problem for the biharmonic equation in the exterior of a compact set under the assumption that solutions of this problem have bounded Dirichlet integrals with the weight $|x|^a$. Depending on the value of the parameter $a$, we obtained uniqueness (non-uniqueness) theorems of the problem and present exact formulas for the dimension of the space of solutions of the mixed Dirichlet–Neumann problem.