Geodesic
The Cauchy problem for a singularly perturbed integro-differential Fredholm equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 4, pp. 655-664

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An initial problem is considered for an ordinary singularly perturbed integro-differential equation with a nonlinear integral Fredholm operator. The case when the reduced equation has a smooth solution is investigated, and the solution to the reduced equation with a corner point is analyzed. The asymptotics of the solution to the Cauchy problem is constructed by the method of boundary functions. The asymptotics is validated by the asymptotic method of differential inequalities developed for a new class of problems. 
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     author = {N. N. Nefedov and A. G. Nikitin},
     title = {The {Cauchy} problem for a~singularly perturbed integro-differential {Fredholm} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {655--664},
     publisher = {mathdoc},
     volume = {47},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_4_a7/}
}
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N. N. Nefedov; A. G. Nikitin. The Cauchy problem for a singularly perturbed integro-differential Fredholm equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 4, pp. 655-664. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_4_a7/