  In this paper, we shall study the Dirichlet problem for the minimal surfaces
equation. We prove some results about the boundary behaviour of a solution of
this problem. We describe the behaviour of a non-converging sequence of
solutions in term of lines of divergence in the domain. Using this second
result, we build some solutions of the Dirichlet problem on unbounded domain.
We then give a new proof of the result of C. Cos\'\i n and A. Ros concerning
the Plateau problem at infinity for horizontal ends.
