A Class of Nonlinear Elliptic Boundary Value Problems
نویسندگان
چکیده
In this paper second order elliptic boundary value problems on bounded domains Ω ⊂ Rn 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 L(Ω) ⊕ (L(∂Ω)), 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.
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