A hypersingular integro-differential equation of the Euler type
https://doi.org/10.29235/1561-2430-2020-56-1-17-29
Abstract
In this paper, we study an integro-differential equation on a closed curve located on the complex plane. The integrals included in the equation are understood as a finite part by Hadamard. The coefficients of the equation have a particular structure. The analytical continuation method is applied. The equation is reduced to a boundary value linear conjugation problem for analytic functions and linear Euler differential equations in the domains of the complex plane. Solutions of the Euler equations, which are unambiguous analytical functions, are sought. The conditions of solvability of the initial equation are given explicitly. The solution of the initial equation obtained under these conditions is also given explicitly. Examples are considered.
About the Author
A. P. Shilin
Belarusian State University
Belarus
Belarus
Andrey P. Shilin – Ph. D. (Physics and Mathematics), Assistant Professor, Assistant Professor of the Department of Higher Mathematics and Mathematical Physics
4, Nezavisimosti Ave., 220030, Minsk
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