Small Oscillations of Ideal Non-Uniform Self-Gravitating Fluid

A problem is considered on small motions of incompressible self-gravitating non-uniform fluid totally filling an arbitrary cavity of the immovable solid body. The theorems are proved on the small motions existence, on the instability of the equilibrium state and also it is proved that the set of wave motion eigenfrequencies of non-uniform incompressible self-gravitating fluid includes an ultimate spectrum.