Solution of the Biharmonic Problem with the Steklov-type and Farwig Boundary Conditions

In this paper, we consider a biharmonic problem with Steklov-type boundary conditions on one part of the boundary and with the Farwig condition on the other part. For this problem, questions of uniqueness of solutions are studied, and in the case of non-uniqueness, provided that the weighted Dirichlet integral is bounded, the exact number of linear independent solutions to the problem under consideration is established. 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.