Geodesic
On the discrete spectrum of a perturbed periodic Schr\"odinger operator
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 19, Tome 190 (1991), pp. 157-162

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A perturbed periodic Schrödinger operator is considered. Conditions for the discrete spectrum in a gap to be finite or infinite are stated. In the case of infinite spectrum a standard asymptotic formula for eigenvalues is justified under certain conditions. The results are formulated in terms of a model problem. 
@article{ZNSL_1991_190_a7,
     author = {S. V. Khryashchev},
     title = {On the discrete spectrum of a perturbed periodic {Schr\"odinger} operator},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {157--162},
     publisher = {mathdoc},
     volume = {190},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_190_a7/}
}
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S. V. Khryashchev. On the discrete spectrum of a perturbed periodic Schr\"odinger operator. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 19, Tome 190 (1991), pp. 157-162. http://geodesic.mathdoc.fr/item/ZNSL_1991_190_a7/