Bocher theorem characterize the behaviour of a positive harmonic function in punctured disc. More precisely if $\Omega$ is a domain in $\mathbb{R}^3$ and $U$ is a non negative solution of $\Delta u=0$ in $B(0,r)\setminus \{0\}$
then $U(x)$ is of the form $U(x)=\frac{a}{|x|}+b(x)$. Is there any similar kind of theorem for higher order Laplacian i.e say for bi-Laplacian $\Delta^2u=0$ or higher order? Any insight is very much appreciated. I can understand the function that satisfies $\Delta u=0$ in $B(0,r)\setminus\{0\}$ would be one candidate but what are all the solutions can one classify like Bocher's theorem? Any insight is very much appreciated.
