Mathematical study of the small oscillations of a pendulum containing an almost homogeneous, incompressible, inviscid liquid and a barotropic gas (Oscillations of a pendulum with almost homogeneous liquid and gas)

The authors study the small oscillations of a pendulum containing an almost homogeneous, incompressible, inviscid liquid (i.e. a liquid whose density in equilibrium is practically a linear function of the height, which differs very little from a constant) and a moving gas. Using functional analysis, they prove that the spectrum is comprised of a countable set of real eigenvalues and an essential spectrum, which fills an interval, and they give an existence and uniqueness theorem for the solution of the evolution problem.