Exterior Biharmonic Problem with the Mixed Steklov and Steklov-Type Boundary Conditions

We study the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Namely, we study the unique solvability of the mixed biharmonic problem with the Steklov and Steklov-type conditions on the boundary in the exterior of a compact set under the assumption that generalized solutions of this problem has a bounded Dirichlet integral with weight vertical bar x vertical bar(a). For solving this biharmonic problem with application we use the variational principle, and depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems or present exact formulas for the dimension of the space of solutions.