Does the following equation imply $u=0$

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Hi I am working on a proof and I ended up with this equation:

$$\int_\limits{\partial \Omega}\alpha u ds + \int_\limits{\Omega} u dx = 0$$

where $\alpha >0$ and $\Omega \subset \mathbb{R}^n$.

Does this imply that $u=0$? If yes, then help me see why. Thanks!