Geodesic
Asymptotics of the eigenvalues of elliptic systems with fast oscillating coefficients
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 33-42

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A singularly perturbed second-order elliptic operator with fast oscillating coefficients is considered in the whole space. Complete asymptotic expansions of the eigenvalues are constructed, which converge to the isolated eigenvalues of the homogenized operator; complete asymptotic expansions for the corresponding eigenfunctions are constructed as well. 
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     author = {D. I. Borisov},
     title = {Asymptotics of the eigenvalues of elliptic systems with fast oscillating coefficients},
     journal = {Trudy Instituta matematiki i mehaniki},
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     publisher = {mathdoc},
     volume = {13},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a2/}
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D. I. Borisov. Asymptotics of the eigenvalues of elliptic systems with fast oscillating coefficients. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 33-42. http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a2/