MATHEMATICAL STUDY OF THE SMALL OSCILLATIONS OF A PENDULUM FILLED BY AN INVISCID, INCOMPRESSIBLE, ALMOST HOMOGENEOUS LIQUID

摘要

The authors study the small oscillations of a pendulum completely filled by an inviscid, incompressible, almost homogeneous liquid. The main object of the paper is to prove that the spectrum is formed by one isolated eigenvalue and an essential spectrum, which fills an interval.