Solution of a nonlinear singular integral equation with quadratic nonlinearity

  • O. V. Gun’ko


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.
How to Cite
Gun’ko, O. V. “Solution of a Nonlinear Singular Integral Equation With Quadratic Nonlinearity”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 5, May 2004, pp. 695-04,
Short communications