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A nonlinear boundary problem. (English) Zbl 0591.30038
The author gives a solution of the nonlinear Hilbert-Gakhov problem $$ [\Phi\sp+(x)]\sp{\alpha}+[\Phi\sp-(x)]\sp{\alpha}=f,\quad 0<x<1,\quad 0<\alpha <1, $$ where f has a derivative satisfying a Hölder condition on [0,1] with the possible exception of the endpoints 0,1. The method of the investigation is based on the reduction to a generalized Abel equation. Reviewer’s remark. The main part of the paper is a solution of the generalized Abel type equation. This equation in detail was investigated in many papers (during the years 1970-74 years) and in the monograph ”Hypersingular integrals and their applications” (1984; Zbl 0577.42016) by {\it S. G. Samko} which is unknown for the author.
Reviewer: N.K.Karapetianc

30E25Boundary value problems, complex analysis
45G05Singular nonlinear integral equations
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