Biharmonic Dirichlet–Farwig problem in exterior domains

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