On boundary control of the Poisson equation with the third boundary condition

This paper studies controllability of the Poisson equation on the unit disk in C subject to the third boundary condition when the control is imposed on the boundary. We use complex analytic methods to prove existence and uniqueness of the control when the parameter λ is a nonzero complex number but not a negative integer (not an eigenvalue). Otherwise, due to multiplicity of solutions to the underlying problem, when λ is a negative integer, controllability could only be obtained if proper additional conditions on the boundary are imposed.