  This paper investigates rotating star solutions to the Euler-Poisson
equations with a non-isentropic equation of state. As a first step, the
equation for gas density with a prescribed entropy and angular velocity
distribution is studied. The resulting elliptic equation is solved either by
the method of sub and supersolutions or by a variational method, depending on
the value of the adiabatic index. The reverse problem of determining angular
velocity from gas density is also considered.
