Geodesic
The discrete spectrum of perturbed differential operators of arbitrary order with periodic matrix coefficients
Matematičeskie zametki, Tome 21 (1977) no. 6, pp. 829-838 
V. I. Khrabustovskii. The discrete spectrum of perturbed differential operators of arbitrary order with periodic matrix coefficients. Matematičeskie zametki, Tome 21 (1977) no. 6, pp. 829-838. http://geodesic.mathdoc.fr/item/MZM_1977_21_6_a9/
@article{MZM_1977_21_6_a9,
     author = {V. I. Khrabustovskii},
     title = {The discrete spectrum of perturbed differential operators of arbitrary order with periodic matrix coefficients},
     journal = {Matemati\v{c}eskie zametki},
     pages = {829--838},
     year = {1977},
     volume = {21},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_6_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For self-adjoint differential operators in $\mathscr L_m^2(R^1)$ of arbitrary order with periodic $(m\times m)$ matrix coefficients, a sufficient condition is obtained for the finiteness of the number of discrete levels arising in a finite spectral gap under the action of a symmetric perturbation affecting all the coefficients.