  We establish unique existence and stability of subsonic potential flow for
steady Euler-Poisson system in a multidimensional nozzle of a finite length
when prescribing the electric potential difference on non-insulated boundary
from a fixed point at the exit, and prescribing the pressure at the exit of the
nozzle. The Euler-Poisson system for subsonic potential flow can be reduced to
a nonlinear elliptic system of second order. In this paper, we develop a
technique to achieve a priori $C^{1,\alp}$ estimates of solutions to a
quasi-linear second order elliptic system with mixed boundary conditions in a
multidimensional domain with Lipschitz continuous boundary. Particularly, we
discovered a special structure of the Euler-Poisson system which enables us to
obtain $C^{1,\alp}$ estimates of velocity potential and electric potential
functions, and this leads us to establish structural stability of subsonic
flows for the Euler-Poisson system under perturbations of various data.
