Geodesic
Perturbation of Solutions with Moving Singularities
Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 3, pp. 401-410

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We study the Cauchy problem for a nonlinear second-order differential equation with a small parameter in the case where the exact solution has a power singularity depending on a small parameter. We propose an asymptotic method similar to the Krylov–Bogoliubov method for localizing the singularity up to the accuracy of any order and construct an asymptotic expansion of the solution in the domain of regular behavior. 
@article{TMF_2001_127_3_a6,
     author = {L. A. Kalyakin},
     title = {Perturbation of {Solutions} with {Moving} {Singularities}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {401--410},
     publisher = {mathdoc},
     volume = {127},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_127_3_a6/}
}
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L. A. Kalyakin. Perturbation of Solutions with Moving Singularities. Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 3, pp. 401-410. http://geodesic.mathdoc.fr/item/TMF_2001_127_3_a6/