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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
Article
  • 20 Downloads

Abstract

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.

Keywords

Integral Equation Analytic Function Entire Function Singular Integral Equation Exponential Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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