Elliptic problems with parameters in the boundary conditions are called Steklov problems. With the tool of computational approximation (finite-element method), we estimate the solution of a nonlinear Steklov eigenvalue problem for a second-order, self-adjoint, elliptic differential problem. We discussed the behavior of the nonlinear problem with the help of computational results using Matlab.
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Kumar, P., Kumar, M. Simulation of a nonlinear Steklov eigenvalue problem using finite-element approximation. Comput Math Model 21, 109–116 (2010). https://doi.org/10.1007/s10598-010-9058-6
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DOI: https://doi.org/10.1007/s10598-010-9058-6