Solution of a nonlinear singular integral equation with quadratic nonlinearity
Using methods of the theory of boundary-value problems for analytic functions, we prove a theorem on the existence of solutions of the equation $$u^2 \left( t \right) + \left( {\frac{1}{\pi }\int\limits_{ - \infty }^\infty {\frac{{u\left( \tau \right)}}{{\tau - t}}d\tau } } \right)^2 = A^2 \left...
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| Datum: | 2004 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2004
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3790 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509922999926784 |
|---|---|
| author | Gun’ko, O. V. Гунько, О. В. Гунько, О. В. |
| author_facet | Gun’ko, O. V. Гунько, О. В. Гунько, О. В. |
| author_sort | Gun’ko, O. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:08:43Z |
| description | Using methods of the theory of boundary-value problems for analytic functions, we prove a theorem on the existence of solutions of the equation
$$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)$$
and determine the general form of a solution by using zeros of an entire function $A^2 (z)$ of exponential type. |
| first_indexed | 2026-03-24T02:48:48Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3790 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:48:48Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/49/70a220dff1ebab4a5aecd0488f83f249.pdf |
| spelling | umjimathkievua-article-37902020-03-18T20:08:43Z Solution of a nonlinear singular integral equation with quadratic nonlinearity Решение нелинейного сингулярного интегрального уравнения с квадратичной нелинейностью Gun’ko, O. V. Гунько, О. В. Гунько, О. В. Using methods of the theory of boundary-value problems for analytic functions, we prove a theorem on the existence of solutions of the equation $$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)$$ and determine the general form of a solution by using zeros of an entire function $A^2 (z)$ of exponential type. Методами теорії крайових задач аналітичних функцій для рівняння $$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)$$ доведено теорему існування розв'язків та одержано запальний вигляд, розв'язку за о допомогою нулів цілої функції експоненціального типу $A^2 (z)$. Institute of Mathematics, NAS of Ukraine 2004-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3790 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 5 (2004); 695-704 Український математичний журнал; Том 56 № 5 (2004); 695-704 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/3790/4301 https://umj.imath.kiev.ua/index.php/umj/article/view/3790/4302 Copyright (c) 2004 Gun’ko O. V. |
| spellingShingle | Gun’ko, O. V. Гунько, О. В. Гунько, О. В. Solution of a nonlinear singular integral equation with quadratic nonlinearity |
| title | Solution of a nonlinear singular integral equation with quadratic nonlinearity |
| title_alt | Решение нелинейного сингулярного интегрального уравнения с квадратичной нелинейностью |
| title_full | Solution of a nonlinear singular integral equation with quadratic nonlinearity |
| title_fullStr | Solution of a nonlinear singular integral equation with quadratic nonlinearity |
| title_full_unstemmed | Solution of a nonlinear singular integral equation with quadratic nonlinearity |
| title_short | Solution of a nonlinear singular integral equation with quadratic nonlinearity |
| title_sort | solution of a nonlinear singular integral equation with quadratic nonlinearity |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3790 |
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