Geodesic
On the spectrum of a~class of differential operators and some imbedding theorems
Izvestiya. Mathematics , Tome 15 (1980) no. 1, pp. 1-24

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The spectral properties of the operator $$ Lu=\frac{(-1)^{n+k}}{\rho(t)}\biggl(\frac{u(t)}{\rho(t)}\biggr)^{(2n+2k)}+\frac{(-1)^k}{\rho(t)}\biggl(V^2(t)\biggl(\frac{u(t)}{\rho(t)}\biggr)^{\!(k)}\biggr)^{\!(k)}\qquad(n,k\geqslant1) $$ are considered. A criterion for the nuclearity of the resolvent, two-sided estimates of the nuclear norm, Green's functions on the diagonal and the norms of the inverse operator are obtained. Bibliography: 21 titles. 
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O. D. Apyshev; M. Otelbaev. On the spectrum of a~class of differential operators and some imbedding theorems. Izvestiya. Mathematics , Tome 15 (1980) no. 1, pp. 1-24. http://geodesic.mathdoc.fr/item/IM2_1980_15_1_a0/