Elliptic boundary value problems with λ-dependent boundary conditions

In this paper second order elliptic boundary value problems on bounded domains with boundary conditions on ∂Ω depending nonlinearly on the spectral parameter are investigated in an operator theoretic framework. For a general class of locally meromorphic functions in the boundary condition a solution operator of the boundary value problem is constructed with the help of a linearization procedure. In the special case of rational Nevanlinna or Riesz–Herglotz functions on the boundary the solution operator is obtained in an explicit form in the product Hilbert space L2(Ω) (L2(∂Ω))m, which is a natural generalization of known results on λ-linear elliptic boundary value problems and λ-rational boundary value problems for ordinary second order differential equations.