A nonlinear boundary problem

Author:
John R. Hatcher

Journal:
Proc. Amer. Math. Soc. **95** (1985), 441-448

MSC:
Primary 30E25; Secondary 45E10

DOI:
https://doi.org/10.1090/S0002-9939-1985-0806084-2

MathSciNet review:
806084

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Abstract: A nonlinear Hilbert problem of power type is solved in closed form by representing a sectionally holomorphic function by means of an integral with power kernel. This technique transforms the problem to one of solving an integral equation of the generalized Abel type.

**[1]**K. D. Sakalyuk,*Abel’s generalized integral equation*, Soviet Math. Dokl.**1**(1960), 332–335. MR**0117520****[2]**N. I. Muskhelishvili,*Singular integral equations*, Wolters-Noordhoff Publishing, Groningen, 1972. Boundary problems of functions theory and their applications to mathematical physics; Revised translation from the Russian, edited by J. R. M. Radok; Reprinted. MR**0355494****[3]**Norman Levinson,*Simplified treatment of integrals of Cauchy type, the Hilbert problem and singular integral equations. Appendix: Poincaré-Bertrand formula*, SIAM Rev.**7**(1965), 474–502. MR**0185398**, https://doi.org/10.1137/1007105**[4]**Wilhelm Magnus, Fritz Oberhettinger, and Raj Pal Soni,*Formulas and theorems for the special functions of mathematical physics*, Third enlarged edition. Die Grundlehren der mathematischen Wissenschaften, Band 52, Springer-Verlag New York, Inc., New York, 1966. MR**0232968**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0806084-2

Keywords:
Cauchy integral,
Plemelj formulae,
nonhomogeneous boundary value problem

Article copyright:
© Copyright 1985
American Mathematical Society