Answer
We would not need to change the electric potential of the central cylinder.
Work Step by Step
To trap a particle with a positive charge in the central cylinder, we can use a trap with the same geometry, and the same electric potential of $V=0$ in the central cylinder.
If the electric potential of the two semi-infinite end cylinders is $-\infty$, then the positron would be attracted to the end cylinders, since the positron has a positive charge.
To trap the positron in the central cylinder, the electric potential of the two semi-infinite end cylinders should be $~~+\infty$
Therefore, we would not need to change the electric potential of the central cylinder.
