11. Let the sequence of positive numbers $a_{0}, a_{1}, a_{2}, \cdots$ satisfy $a_{0}=a_{1}=1$ and $\sqrt{a_{n} a_{n-2}}-\sqrt{a_{n-1} a_{n-2}}=2 a_{n-1}, n=2,3, \cdots$, find the general term formula of this sequence.
11. Since when $n \geqslant 2$, $\sqrt{a_{n}}=\sqrt{a_{n-1}}+\frac{2 a_{n-1}}{\sqrt{a_{n-2}}}$.

Let $b_{n}=\sqrt{\frac{a_{n}}{a_{n-1}}}$, then $b_{1}=1$, and $b_{n}=1+2 b_{n-1}, n=2,3, \cdots$ It is easy to get $b_{n}=2^{n}-1, n=1,2, \cdots$ Therefore, $\sqrt{a_{n}}=\left(2^{n}-1\right) \sqrt{a_{n-1}}$, and the general term formula is $a_{n}=\prod_{k=1}^{n}\left(2^{k}-1\right)^{2}, n=1,2,3, \cdots$