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#### OliviaB

I think this is Poisson's Equation (and inhomogenous). I think I need to use Green's Identity.

Let $\mathcal{R}$ be a bounded region in $\mathbb{R}^3$, and suppose $p(x) > 0$ on $\mathcal{R}$.

(i) If $u$ is a solution of

$\bigtriangledown^2 u = p(x) u \ \ x \in \mathcal{R} \ \ \bigtriangledown \cdot n = 0 \ \x \in \partial \mathcal{R}$

show that $u \equiv 0$ on $\mathcal{R}$

(ii) If $u$ is a solution of

$\bigtriangledown^2 u = p(x) u \ \ x \in \mathcal{R} \ \ \bigtriangledown \cdot n = g(x) \ \x \in \partial \mathcal{R}$

show that $u$ is unique (It can be assumed that part (i) is true).

I dont know how to start this...

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