2018
Том 70
№ 4

All Issues

Gun’ko O. V.

Articles: 1
Brief Communications (Russian)

Solution of a nonlinear singular integral equation with quadratic nonlinearity

Gun’ko O. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 5. - pp. 695-704

Using methods of the theory of boundary-value problems for analytic functions, we prove a theorem on the existence of solutions of the equation $$u^2 \left( t \right) + \left( {\frac{1}{\pi }\int\limits_{ - \infty }^\infty {\frac{{u\left( \tau \right)}}{{\tau - t}}d\tau } } \right)^2 = A^2 \left( t \right)$$ and determine the general form of a solution by using zeros of an entire function $A^2 (z)$ of exponential type.