摘要:  I will discuss some recent results (with Chongchun Zeng) on stability criterion for non-rotating gaseous stars modeled by the Euler-Poisson

system. Under general assumptions on the equation of states, we prove a turning point principle that the stability of the stars is entirely

determined by the mass-radius curve parametrized by the center density. In particular, the stability can only changed at points with an extremal mass. We use a combination of first order and 2nd order Hamiltonian formulations to get the stability criterion and the semi-group estimates for the linearized equation. If time permits, I will briefly describe the extension of this approach to study stability of rotating stars, and relativistic stars and star clusters.