Solution
= Solution
Yes. Since $|q|\leq\mu$ and $u\geq0$,
$$
(\Delta-\mu)u=(\Delta u+qu)-(q+\mu)u\leq0.
$$
The operator $\Delta-\mu$ is uniformly elliptic and has nonpositive zeroth-order coefficient. If $u(y)=0$ at an interior point, $u$ attains its nonnegative minimum there, so the <strong minimum principle for elliptic operators> gives $u\equiv0$ on the connected ball $B_1$.