On the approximation solvability of a class of strongly nonlinear elliptic problems on unbounded domains Original Research Article

A class of strongly nonlinear boundary value problems posed on unbounded regions is considered. A nonlocal coupling of the linearized far-field exterior to an auxiliary boundary allows for approximations to be defined on domains of finite extent. Constructive existence results for bounded domains are then extended by employing an exhausting sequence of approximating domains. In particular, well-posedness is seen to be equivalent to unique approximation solvability, with the rate of convergence dependent upon the radius of the auxiliary boundary. Application to a model of proteins immersed in an electrolyte solution is made.