Spectral properties of the Sturm-Liouville operator with a parameter that changes sign and their usage to the study of the spectrum of differential operators of mathematical physics belonging to different types

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In this paper, for the Sturm-Liouville operator with a parameter that changes sign the following results: 1) the existence of the resolvent, 2) the criterion of the spectrum discreteness, 3) two-sided estimates of approximation numbers (s-numbers) are obtained. These results are applied to the study of the spectral properties of differential operators of elliptic, parabolic and hyperbolic types.