11. (20 points) Given positive real numbers $p, q$. It is known that the sequence of positive real numbers $\left\{a_{n}\right\}$ satisfies:
$$
a_{0}=1, a_{n+2}=p a_{n}-q a_{n+1}(n \in \mathbf{N}) .
$$

Find all possible values of $a_{1}$ (expressed in terms of $p, q$).