Geodesic
Theory of singular perturbations with a non-smooth spectrum of the limit operator
Sbornik. Mathematics, Tome 186 (1995) no. 7, pp. 951-966 
A. G. Eliseev. Theory of singular perturbations with a non-smooth spectrum of the limit operator. Sbornik. Mathematics, Tome 186 (1995) no. 7, pp. 951-966. http://geodesic.mathdoc.fr/item/SM_1995_186_7_a2/
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     title = {Theory of singular perturbations with a~non-smooth spectrum of the~limit operator},
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Voir la notice de l'article provenant de la source Math-Net.Ru

This work is devoted to the development of the regularization method [1] for the case where the spectrum of the limit variable operator has non-smooth singularities. The case will be investigated where one of the eigenvalues of the limit operator $A(t)$ vanishes identically on certain sections of the segment [0, T], and the approach to these sections has a polynomial singularity. Such problems arise in the radio and impulse technologies.

[1] Lomov S. A., Vvedenie v obschuyu teoriyu singulyarnykh vozmuschenii, Nauka, M., 1981 | MR

[2] Eliseev A. G., Lomov S. A., “Teoriya singulyarnykh vozmuschenii v sluchae spektralnykh osobennostei predelnogo operatora”, Matem. sb., 131(173):4(12) (1986), 544–557 | MR | Zbl

[3] Gantmakher F. R., Teoriya matrits, Nauka, M., 1967 | MR

[4] Sadovnichii V. A., Teoriya operatorov, Izd-vo MGU, M., 1979 | MR | Zbl

[5] Filippov A. F., Differentsialnye uravneniya s razryvnoi pravoi chastyu, Nauka, M., 1985 | MR