Non-Isentropic Multi-Transonic Solution Of Euler-Poisson System

In this paper,we consider the boundary value problem of the one-dimensional steady non-isentropic Euler-Poisson system.In the one dimensional straight nozzles,the physical subsonic inflow and outflow conditions are prescribed at boundaries.We'll prove the existence of multi-transonic solution and the solution contains shock,i.e.,we'll prove the existence of subsonic-sonic-supersonic-shock-subsonic flows in one-dimensional straight nozzles.Furthermore,the monotonicity between the location of the transonic shock and the density at the exit of the nozzle will be elucidated.