  For the stationary hydrodynamic model for semiconductors with sonic boundary,
represented by Euler-Poisson equations, it possesses the various physical
solutions including interior subsonic solutions/interior supersonic
solutions/shock transonic solutions/$C^1$-smooth transonic solutions. However,
the structural stability for these physical solutions is challenging and has
remained open as we know. In this paper, we investigate the structural
stability of interior subsonic solutions when the doping profiles are
restricted in the subsonic region. The main result is proved by using the local
(weighted) singularity analysis and the monotonicity argument. Both the result
itself and techniques developed here will give us some truly enlightening
insights into our follow-up study on the structural stability of the remaining
types of solutions.
