Geodesic
The theory of perturbations for a polyharmonic operator with non-smooth periodic potential
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 8, Tome 169 (1988), pp. 76-83

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In space $L_2(R^n)$, $n>1$ is considered operator $H_\alpha=(-\Delta)^\ell+\alpha V$, $\alpha\in[-1,1]$, $4\ell>n+1$, $V$ – real, periodical potential. She convergent series of perturbation theory for the eigenfunctions and eigenvalues on the rich set of kvasiimpulse are constructed. 
@article{ZNSL_1988_169_a8,
     author = {Yu. E. Karpeshina},
     title = {The theory of perturbations for a polyharmonic operator with non-smooth periodic potential},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {76--83},
     publisher = {mathdoc},
     volume = {169},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_169_a8/}
}
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Yu. E. Karpeshina. The theory of perturbations for a polyharmonic operator with non-smooth periodic potential. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 8, Tome 169 (1988), pp. 76-83. http://geodesic.mathdoc.fr/item/ZNSL_1988_169_a8/