One class of solutions of Volterra equations with regular singularity
The Volterra integral equation of the second order with a regular singularity is considered. Under the conditions that a kernel K(x,t) is a real matrix function of order n×n with continuous partial derivatives up to order N+1 inclusively and K(0,0) has complex eigenvalues ν±i μ (ν>0), it is s...
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| Date: | 1997 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5015 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511210463559680 |
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| author | Krein, S. G. Sapronov, I. V. Крейн, С. Г. Сапронов, І. В. |
| author_facet | Krein, S. G. Sapronov, I. V. Крейн, С. Г. Сапронов, І. В. |
| author_sort | Krein, S. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:22:53Z |
| description | The Volterra integral equation of the second order with a regular singularity is considered. Under the conditions that a kernel K(x,t) is a real matrix function of order n×n with continuous partial derivatives up to order N+1 inclusively and K(0,0) has complex eigenvalues ν±i μ (ν>0), it is shown that if ν>2|‖K|‖ C -N-1, then a given equation has two linearly independent solutions. |
| first_indexed | 2026-03-24T03:09:16Z |
| format | Article |
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| id | umjimathkievua-article-5015 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:09:16Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/75/889381e7fb7c7b7ccf8d5cae135ee375.pdf |
| spelling | umjimathkievua-article-50152020-03-18T21:22:53Z One class of solutions of Volterra equations with regular singularity Про один клас розв'язків рівняння Вольтерра з регулярною сингулярністю Krein, S. G. Sapronov, I. V. Крейн, С. Г. Сапронов, І. В. The Volterra integral equation of the second order with a regular singularity is considered. Under the conditions that a kernel K(x,t) is a real matrix function of order n×n with continuous partial derivatives up to order N+1 inclusively and K(0,0) has complex eigenvalues ν±i μ (ν>0), it is shown that if ν>2|‖K|‖ C -N-1, then a given equation has two linearly independent solutions. Розглядається інтегральне рівняння Вольтерра другого роду з регулярного сипгулярністю. У припущенні, що ядро K(x,t) —дійсна матричпозпачна функція порядку n×n з неперервними частинними похідними до порядку N+1 включно, і K(0,0) має комплексні власні значення ν±i μ (ν>0). Показано, що коли ν>2|‖K|‖ C -N-1, тоді існують два лінійно незалежних розв'язки даного рівняння. Institute of Mathematics, NAS of Ukraine 1997-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5015 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 3 (1997); 424–432 Український математичний журнал; Том 49 № 3 (1997); 424–432 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/5015/6729 https://umj.imath.kiev.ua/index.php/umj/article/view/5015/6730 Copyright (c) 1997 Krein S. G.; Sapronov I. V. |
| spellingShingle | Krein, S. G. Sapronov, I. V. Крейн, С. Г. Сапронов, І. В. One class of solutions of Volterra equations with regular singularity |
| title | One class of solutions of Volterra equations with regular singularity |
| title_alt | Про один клас розв'язків рівняння Вольтерра з регулярною сингулярністю |
| title_full | One class of solutions of Volterra equations with regular singularity |
| title_fullStr | One class of solutions of Volterra equations with regular singularity |
| title_full_unstemmed | One class of solutions of Volterra equations with regular singularity |
| title_short | One class of solutions of Volterra equations with regular singularity |
| title_sort | one class of solutions of volterra equations with regular singularity |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5015 |
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