Use principle of minimum maximum for te equation of Laplace, for prove the solution of the problem homogeneous is:
\begin{eqnarray} \Delta u=0 \,\,\,\, \text{in} \,\,\Omega\atop u=0 \,\,\,\, \text{on }\,\, \partial\Omega \end{eqnarray}
is the trivial solution.
I don't have a clear idea of how solve this type of exercise. Can someone help me with this?