Uniqueness for an elliptic problem

Question

I want to prove the uniqueness of the solution of the following problem: $$\eqalign{ & - d\Delta u + u = {u^p}{\text{ in }}\Omega \cr & u > 0{\text{ in }}\Omega \cr & \frac{{\partial u}}{{\partial \nu }} = 0{\text{ on }}\partial \Omega \cr} $$ with $\Omega$ is a bounded open in $R^n$, d$>0$ and $p>1$. I tried the classical methods but without any success. Thanx.