Ukrainian Mathematical Journal

, Volume 56, Issue 5, pp 840–851 | Cite as

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 A2 (z) of exponential type.


Integral Equation Analytic Function Entire Function Singular Integral Equation Exponential Type 
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Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • O. V. Gun’ko
    • 1
  1. 1.Kharkov Military UniversityKharkov

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