Unstable Galaxy Models
  The dynamics of collisionless galaxy can be described by the Vlasov-Poisson
system. By the Jean's theorem, all the spherically symmetric steady galaxy
models are given by a distribution of {\Phi}(E,L), where E is the particle
energy and L the angular momentum. In a celebrated Doremus-Feix-Baumann
Theorem, the galaxy model {\Phi}(E,L) is stable if the distribution {\Phi} is
monotonically decreasing with respect to the particle energy E. On the other
hand, the stability of {\Phi}(E,L) remains largely open otherwise. Based on a
recent abstract instability criterion of Guo-Lin, we constuct examples of
unstable galaxy models of f(E,L) and f(E) in which f fails to be monotone in E.
