Abstract In this paper, we generalized B. Merouani's [10], M. Dilmi's [5] and P. Grisvard's [7] works in the case when the Lame's system is perturbed with Diriclet boundary condition on one part and non linear condition one on the other part. To achieve this goal, we consider the approached problem and we solved this last problem by using Brézi's contraction metho