Sturm–Liouville operator with a parameter and its usage to spectrum research of some differential operators
Mussakan B. Muratbekov, Madi M. Muratbekov, M. M. Muratbekov, M. M. Muratbekov · Complex Variables and Elliptic Equations · 2018
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.