Uniqueness of stationary solutions with vacuum of Euler-Poisson equations

In this paper, the uniqueness of stationary solutions with vacuum of Euler-Poisson equations is considered. Through a nonlinear transformation which is a function of density and entropy, the corresponding problem cam be reduced to a semilinear elliptic equation with a nonlinear source term consisting of a power function, for which the classical theory([4],[9]) of the elliptic equations leads the authors to the uniqueness result under some assumptions on the entropy function S(x). As an example, the authors get the uniqueness of stationary solutions with vacuum of Euler-Poisson equations for S(x) = \x\(theta) and theta is an element of {0}boolean OR(2(N-2), + infinity).