Biharmonic Problem with Steklov-type Conditions on the Boundary of the Domain

This paper considers a biharmonic problem with a Steklov-type boundary condition on the boundary. For this problem, questions of both uniqueness and non-uniqueness of solutions are studied under the condition that the weighted Dirichlet integral is bounded, and for which 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 solution space depending on the value of the parameter included in the weighted Dirichlet integral.