In this article, we study the existence and uniqueness of solutions for nonlinear elliptic problems with non-local boundary conditions. In order to get the unique solution, we study first an auxiliary problem, for which we deduce useful a priori estimates. The study of the auxiliary problem gives us the equivalence between this kind of problem and a nonlinear problem with very large diffusion around the boundary.

Leray–Lions type operator non-local boundary conditions operator of type M standard monotonicity arguments.