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The stability of oscillations of an ideal conducting shell with a longitudinal current containing the flow of an ideal incompressible fluid with respect to radial disturbance of the shape of the shell is studied.

For the Sturm-Louville equation with block-triangular matrix potential that increases at infinity, both increasing and decreasing at infinity matrix solutions are found. The structure of spectrum for the differential operator with these coefficients is defined.Key words: differential operator, spectrum, block-triangular matrix coefficients.Mathematics Subject Classification 2010: 34K11, 47A10. Dedicated to our Teacher, Academician Vladimir A. Marchenko on the occasion of his 90th birthday, with appreciation and admiration for his contribution to spectral theory, differential equations and mathematical physicsThe study of the relationship between spectral and oscillation properties of non-selfadjoint differential operators with block-triangular matrix coefficients that increase at infinity [1] includes the study of the structure of the spectra of these operators. For the case of an operator with decreasing at infinity triangular matrix potential and a bounded first moment, the structure of the spectrum in the context of the inverse scattering problem was established in [2][3][4].In [5,6], V.A. Marchenko introduced a notion of the generalized spectral function R for a Sturm-Liouville operator with arbitrary complex valued potential on the semiaxis. This result was generalized to the case of non-selfadjoint systems [7,8]. The distribution (the matrix one in the case of systems) acts on c A.M. Kholkin and F.S. Rofe-Beketov, 2014

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