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Suppose that $v$ is critical point of $$ f(u)=\frac{1}{2} \int_D|\nabla u|^2-\frac{1}{p+1} \int_D|u|^{p+1}, \quad u \in H_{0, \text{rad}}^1(D),\quad D(r, d)=\left\{z \in R^N: r^2<|z|^2<(r+d)^2\...