Conditions of solvability of quasilinear periodic boundary-value problems for hyperbolic equations of the second order
On the basis of properties of the Vejvoda-Shtedry operator, we obtain solvability conditions for the 2π-periodic problem $$u_{tt} - u_{xx} = F\left[ {u,u_t } \right], u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0, u\left( {x,t + 2\pi } \right) = u\left( {x,t} \right)$$ .
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| Date: | 1998 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1998
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4892 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511072675430400 |
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| author | Mitropolskiy, Yu. A. Khoma, N. H. Khoma, G. P. Митропольский, Ю. А. Хома, H. Г. Хома, Г. П. Митропольский, Ю. А. Хома, H. Г. Хома, Г. П. |
| author_facet | Mitropolskiy, Yu. A. Khoma, N. H. Khoma, G. P. Митропольский, Ю. А. Хома, H. Г. Хома, Г. П. Митропольский, Ю. А. Хома, H. Г. Хома, Г. П. |
| author_sort | Mitropolskiy, Yu. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:16:32Z |
| description | On the basis of properties of the Vejvoda-Shtedry operator, we obtain solvability conditions for the 2π-periodic problem $$u_{tt} - u_{xx} = F\left[ {u,u_t } \right], u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0, u\left( {x,t + 2\pi } \right) = u\left( {x,t} \right)$$ . |
| first_indexed | 2026-03-24T03:07:05Z |
| format | Article |
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| id | umjimathkievua-article-4892 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:07:05Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/31/e749920b61d89cd0a09a7b0134b7dc31.pdf |
| spelling | umjimathkievua-article-48922020-03-18T21:16:32Z Conditions of solvability of quasilinear periodic boundary-value problems for hyperbolic equations of the second order Условия разрешимости квазилинейных краевых периодических задач для гиперболического уравнения второго порядка Mitropolskiy, Yu. A. Khoma, N. H. Khoma, G. P. Митропольский, Ю. А. Хома, H. Г. Хома, Г. П. Митропольский, Ю. А. Хома, H. Г. Хома, Г. П. On the basis of properties of the Vejvoda-Shtedry operator, we obtain solvability conditions for the 2π-periodic problem $$u_{tt} - u_{xx} = F\left[ {u,u_t } \right], u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0, u\left( {x,t + 2\pi } \right) = u\left( {x,t} \right)$$ . На основі властивостей оператора Вейводи-Штедри одержано умови розв'язності $2π$ -періодичної задачі $$u_{tt} - u_{xx} = F\left[ {u,u_t } \right], u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0, u\left( {x,t + 2\pi } \right) = u\left( {x,t} \right).$$ Institute of Mathematics, NAS of Ukraine 1998-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4892 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 6 (1998); 818–821 Український математичний журнал; Том 50 № 6 (1998); 818–821 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4892/6483 https://umj.imath.kiev.ua/index.php/umj/article/view/4892/6484 Copyright (c) 1998 Mitropolskiy Yu. A.; Khoma N. H.; Khoma G. P. |
| spellingShingle | Mitropolskiy, Yu. A. Khoma, N. H. Khoma, G. P. Митропольский, Ю. А. Хома, H. Г. Хома, Г. П. Митропольский, Ю. А. Хома, H. Г. Хома, Г. П. Conditions of solvability of quasilinear periodic boundary-value problems for hyperbolic equations of the second order |
| title | Conditions of solvability of quasilinear periodic boundary-value problems for hyperbolic equations of the second order |
| title_alt | Условия разрешимости квазилинейных краевых периодических задач для гиперболического уравнения второго порядка |
| title_full | Conditions of solvability of quasilinear periodic boundary-value problems for hyperbolic equations of the second order |
| title_fullStr | Conditions of solvability of quasilinear periodic boundary-value problems for hyperbolic equations of the second order |
| title_full_unstemmed | Conditions of solvability of quasilinear periodic boundary-value problems for hyperbolic equations of the second order |
| title_short | Conditions of solvability of quasilinear periodic boundary-value problems for hyperbolic equations of the second order |
| title_sort | conditions of solvability of quasilinear periodic boundary-value problems for hyperbolic equations of the second order |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4892 |
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