Steklov Biharmonic Problem with Weighted Dirichlet Integral

We consider the Steklov biharmonic problem with the boundary conditions with parameters in the exterior of a compact set under the assumption that the generalized solutions of this problem have a bounded weighted Dirichlet integral. Using the variational principle, uniqueness (non-uniqueness) theorems are obtained, as well as exact formulas for calculating the dimension of the space of solutions depending on the value of the parameter included in the weighted Dirichlet integral.