Spectral properties of quadratic beams of operators, connected with stability problems

Abstract

The investigation in the field of functional analysis is considered in the paper aiming at the obtaining of some results about the summary algebraic spectrum ratio in an open right half-plane for quadratic beams of non-bounded operators. The investigation of the dependence of critical values of beams on some parameters is also the aim of the paper. Some results of the spectrum localization of some quadratic beams have been obtained. The theorem of the stability for one class of differential equations in Hilbert space has been proved. The lower estimation of a critical value, under which the problem loses its stability, has been found. The paper results may find their field of application in spectral theory, elasticity and hydrodynamics theoryAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio