We deal with a PDE problem with a polynomial Robin boundary condition. We prove the existence and unicity of solution of the problem and we propose an iterative method allowing the construction of the solution. The proposed method is a generalization of a result recently proved by Benameur and Elhechmi [3].

In [2] M. Jaoua et al. studied the linear approximation of Robin problem on Ω an open bounded domain of R d , and they given some important results. In this paper, we study a nonlinear approximation of an elliptic problem with a nonlinear Robin boundary condition in a domain of R 2 . We prove the existence and uniqueness of solution by an iterative construction method with admissible condition on ∂Ω.