Geodesic
Justification of asymptotic expansions of the eigenvalues of nonselfadjoint singularly perturbed elliptic boundary value problems
Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 317-349

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Boundary value problems for scalar elliptic equations are considered with a small parameter $\varepsilon$ in front of the leading derivatives in domains with a smooth boundary. As $\varepsilon\to0$ this problem degenerates in a regular way into an elliptic problem of lower order. Neither problem is assumed to be selfadjoint. Formal asymptotic expansions of the eigenvalues and eigenfunctions of the singularly perturbed spectral problem are justified under assumptions regarding the initial problem and the limit problem. Bibliography: 16 titles. 
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     author = {S. A. Nazarov},
     title = {Justification of asymptotic expansions of the eigenvalues of nonselfadjoint singularly perturbed elliptic boundary value problems},
     journal = {Sbornik. Mathematics},
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     volume = {57},
     number = {2},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_57_2_a0/}
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S. A. Nazarov. Justification of asymptotic expansions of the eigenvalues of nonselfadjoint singularly perturbed elliptic boundary value problems. Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 317-349. http://geodesic.mathdoc.fr/item/SM_1987_57_2_a0/