Geodesic
Asymptotic behavior of the solution of a singular integral equation with a small parameter
Sbornik. Mathematics, Tome 29 (1976) no. 3, pp. 411-429 
V. Yu. Novokshenov. Asymptotic behavior of the solution of a singular integral equation with a small parameter. Sbornik. Mathematics, Tome 29 (1976) no. 3, pp. 411-429. http://geodesic.mathdoc.fr/item/SM_1976_29_3_a8/
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     title = {Asymptotic behavior of the solution of a~singular integral equation with a~small parameter},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We construct an asymptotic expansion as $h\to0$ that is uniform in $x\geqslant0$ of the solution of the singular integral equation $$ \int^\infty_0\frac{\rho(t)}{x-t}\,dt+\int^\infty_0K(x-t,h)\rho(t)\,dt=f(x). $$ Bibliography: 3 titles.

[1] N. I. Muskhelishvili, Singulyarnye integralnye uravneniya, izd-vo «Nauka», Moskva, 1968 | MR

[2] M. G. Krein, “Integralnye uravneniya na poluosi s yadrom, zavisyaschim ot raznosti argumentov”, Uspekhi matem. nauk, XIII:5 (83) (1958), 3–118 | MR

[3] Dzh. Khirt, I. Lote, Teoriya dislokatsii, izd-vo «Atomizdat», Moskva, 1972