I have been trying to show that the weak solution $\displaystyle u \in H^1(\Omega) $ such that

$\displaystyle \displaystyle\int_\Omega \nabla u . \nabla v + \alpha + \displaystyle\int_{\partial\Omega} uv = \displaystyle\int_\Omega vf $ for all $\displaystyle v \in H^1(\Omega) $

is unique. I have been told this is hard. I could use Lax-Milgram to show existance and uniqueness but am finding it hard to show coercivity and continuity... any ideas... I only have to show uniqueness, not existence...