Operators approaches in studying the problem on normal oscillations of system of m capillary viscous fluid

Our aim of this paper is studying the problem on normal oscillations of system of capillary viscous fluids in vessel. We prove results about the spectrum of the problem for rotating vessel and prove that the systems of root elements ( eigenelements and associated elements ) form an Abel-Lidsky basis. Also , we use some results from the theory of J-self adjoint operators in studying the spectrum of the problem for non-rotating vessel.