Solution of a nonlinear singular integral equation with quadratic nonlinearity

• Datum: 2004
• Hauptverfasser: Gun’ko, O. V., Гунько, О. В.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2004
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3790
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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...