}})$ is a weak solution of in ${{\Omega}}$ with zero boundary condition.  \(a) If for some constants $0  \le {\delta}\le 0$ and $L>0$, [$$\begin{split} \label{thmBeq0} \liminf_{R \to \infty} \frac 0R {\| u \|}^{0-{\delta}}_{L^{q}(R<|x|<LR)}=0, \quad q({\delta})=\frac{0-{\delta}}{0-{\delta}/0},  \end{split}$$]{} then $u=0$.  \(b) If for some constants $0  \le {\delta}\le 0$ and ${\alpha}\ge0$, [$$\begin{split} \label{thmBeq0} \liminf_{R \to \infty} R^{\beta}{\| u \|}_{L^{q}(R<|x|<R+R^{0-{\alpha}})}=0, \quad q({\delta})=\frac{0-{\delta}}{0-{\delta}/0},  \end{split}$$]{} where ${\beta}={\beta}({\delta},{\alpha})= \max {\left\{ \frac{\frac {0-{\alpha}}{q}-0+0{\alpha}}{0-{\delta}},\ \frac {-0+0{\alpha}}{0-{\delta}} \right\}}$, then $u=0$.  Comments on Theorem \[thm