Geodesic
Small solutions of nonlinear differential equations near branching points
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 53-61

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We construct parametric families of small branching solutions to nonlinear differential equations of the $n$th order near branching points. We use methods of the analytical theory of branching solutions of nonlinear equations and the theory of differential equations with a regular singular point. We illustrate the general existence theorems with an example of a nonlinear differential equation in a certain magnetic insulation problem.
Keywords: Newton diagram, Jordan forms, Euler operator, branching, contracted mapping. 
@article{IVM_2011_5_a6,
     author = {N. A. Sidorov and D. N. Sidorov},
     title = {Small solutions of nonlinear differential equations near branching points},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {53--61},
     publisher = {mathdoc},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_5_a6/}
}
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N. A. Sidorov; D. N. Sidorov. Small solutions of nonlinear differential equations near branching points. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 53-61. http://geodesic.mathdoc.fr/item/IVM_2011_5_a6/