Geodesic
On successive approximations of solutions of a~singular Cauchy problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 238-244

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Solutions of the Cauchy problem for a differential equation with a Fredholm operator in the main part are constructed by successive approximations, which converge uniformly in a neighborhood of algebraic branch points. The leading term of the asymptotics is constructed with the help of the analytical theory of branching solutions of operator equations. It is employed as the initial approximation.
Keywords: Cauchy problem, Fredholm operator, branching of solutions, asymptotics, successive approximations. 
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N. A. Sidorov; D. N. Sidorov. On successive approximations of solutions of a~singular Cauchy problem. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 238-244. http://geodesic.mathdoc.fr/item/TIMM_2012_18_2_a22/