Geodesic
Successive approximations to solutions of nonlinear equations with vector parameter in the irregular case
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 132-137

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We consider a nonlinear operator equation with a Fredholm operator in the principal part. The nonlinear part of the equation depends on some functionals that are defined on an open set of a normed linear space. We suggest a method of successive asymptotic approximations to branching solutions. We apply this method to study a nonlinear boundary value problem describing the oscillation of a satellite in the plane of its elliptic orbit.
Keywords: branching of solutions, Fredholm operator, asymptotics, Trenogin's regularizer, successive approximations. 
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     author = {N. A. Sidorov and D. N. Sidorov and R. Yu. Leont'ev},
     title = {Successive approximations to solutions of nonlinear equations with vector parameter in the irregular case},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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N. A. Sidorov; D. N. Sidorov; R. Yu. Leont'ev. Successive approximations to solutions of nonlinear equations with vector parameter in the irregular case. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 132-137. http://geodesic.mathdoc.fr/item/SJIM_2012_15_1_a12/