Geodesic
Unique Solvability of Singularly Perturbed Boundary-Value Problems with Unstable Spectrum of the Limit Operator
Matematičeskie zametki, Tome 95 (2014) no. 2, pp. 222-226.

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The paper contains an asymptotic study of solutions of singularly perturbed boundary-value problems in the case of a limit operator with unstable spectrum. The main singularities of the solution are described and the principal term of the asymptotics is constructed.
Keywords: singularly perturbed boundary-value problem, unstable spectrum of the limit operator, regularization method, nonlocal boundary-value problem, turning point. 
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     title = {Unique {Solvability} of {Singularly} {Perturbed} {Boundary-Value} {Problems} with {Unstable} {Spectrum} of the {Limit} {Operator}},
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A. G. Eliseev; Yu. A. Konyaev; D. A. Shaposhnikova. Unique Solvability of Singularly Perturbed Boundary-Value Problems with Unstable Spectrum of the Limit Operator. Matematičeskie zametki, Tome 95 (2014) no. 2, pp. 222-226. http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a4/

[1] V. P. Maslov, Kompleksnyi metod VKB v nelineinykh uravneniyakh, Nelineinyi analiz i ego prilozheniya, Nauka, M., 1977 | MR | Zbl

[2] A. Kh. Naife, Metody vozmuschenii, Mir, M., 1976 | MR

[3] A. B. Vasileva, V. F. Butuzov, Asimptoticheskie razlozheniya reshenii singulyarno vozmuschennykh uravnenii, Nauka, M., 1973 | MR | Zbl

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

[5] V. F. Safonov, A. A. Bobodzhanov, Singulyarno vozmuschennye zadachi i metod regulyarizatsii, Izd-vo MEI, M., 2010

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

[7] Yu. A. Konyaev, “O nekotorykh metodakh issledovaniya ustoichivosti”, Matem. sb., 192:3 (2001), 65–82 | DOI | MR | Zbl

[8] Yu. A. Konyaev, “Ob odnoznachnoi razreshimosti nekotorykh klassov nelineinykh regulyarnykh i singulyarno vozmuschennykh kraevykh zadach”, Differents. uravneniya, 35:8 (1999), 1028–1035 | MR | Zbl