Multiple solutions to boundary-value problems for fourth-order elliptic equations
UDC 517.9 We study the existence of multiple solutions for the biharmonic problem\begin{gather*}\Delta^2 u = f(x, u) + g(x, u)\quad \mbox{in}\quad \Omega,\\ u = \partial_\nu u = 0\quad \text{on}\quad \partial\Omega,\end{gather*} where $\Omega$ is a bounded domain with smooth boundary in $\mathbb{R}^...
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| Дата: | 2023 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2023
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/6958 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512559628550144 |
|---|---|
| author | Luyen, Duong Trong Trang, Mai Thi Thu Luyen, Duong Trong Trang, Mai Thi Thu |
| author_facet | Luyen, Duong Trong Trang, Mai Thi Thu Luyen, Duong Trong Trang, Mai Thi Thu |
| author_sort | Luyen, Duong Trong |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-07-02T07:08:10Z |
| description | UDC 517.9
We study the existence of multiple solutions for the biharmonic problem\begin{gather*}\Delta^2 u = f(x, u) + g(x, u)\quad \mbox{in}\quad \Omega,\\ u = \partial_\nu u = 0\quad \text{on}\quad \partial\Omega,\end{gather*} where $\Omega$ is a bounded domain with smooth boundary in $\mathbb{R}^N,$ $ N >4,$ $f(x, \xi)$ is odd in $\xi,$ and $g(x, \xi)$ is a perturbation term. Under certain growth conditions on $f$ and $g,$ we show that there are infinitely many weak solutions to the problem. |
| doi_str_mv | 10.37863/umzh.v75i6.6958 |
| first_indexed | 2026-03-24T03:30:43Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6958 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:30:43Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-69582023-07-02T07:08:10Z Multiple solutions to boundary-value problems for fourth-order elliptic equations Multiple solutions to boundary-value problems for fourth-order elliptic equations Luyen, Duong Trong Trang, Mai Thi Thu Luyen, Duong Trong Trang, Mai Thi Thu Biharmonic, boundary value problems, critical points, perturbation methods, multiple solutions. Primary 35J60; Secondary 35B33, 35J25, 35J70 UDC 517.9 We study the existence of multiple solutions for the biharmonic problem\begin{gather*}\Delta^2 u = f(x, u) + g(x, u)\quad \mbox{in}\quad \Omega,\\ u = \partial_\nu u = 0\quad \text{on}\quad \partial\Omega,\end{gather*} where $\Omega$ is a bounded domain with smooth boundary in $\mathbb{R}^N,$ $ N >4,$ $f(x, \xi)$ is odd in $\xi,$ and $g(x, \xi)$ is a perturbation term. Under certain growth conditions on $f$ and $g,$ we show that there are infinitely many weak solutions to the problem. УДК 517.9 Численні розв’язки крайових задач для еліптичних рівнянь четвертого порядку Досліджено існування кількох розв’язків бігармонічної задачі\begin{gather*}\Delta^2 u = f(x, u) + g(x, u)\quad \mbox{в}\quad \Omega,\\ u = \partial_\nu u = 0\quad \text{на}\quad \partial\Omega,\end{gather*} де $\Omega$ – обмежена область із гладкою межею в $\mathbb{R}^N,$ $ N >4,$ $f(x, \xi)$ непарна по $\xi,$ а $g( x, \xi)$ – член збурення.  За деяких умов, накладених на зростання  $f$ і $g,$  показано, що існує нескінченна кількість слабких розв’язків задачі. Institute of Mathematics, NAS of Ukraine 2023-06-20 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/6958 10.37863/umzh.v75i6.6958 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 6 (2023); 830 - 841 Український математичний журнал; Том 75 № 6 (2023); 830 - 841 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6958/9766 Copyright (c) 2023 Duong Trong Luyen |
| spellingShingle | Luyen, Duong Trong Trang, Mai Thi Thu Luyen, Duong Trong Trang, Mai Thi Thu Multiple solutions to boundary-value problems for fourth-order elliptic equations |
| title | Multiple solutions to boundary-value problems for fourth-order elliptic equations |
| title_alt | Multiple solutions to boundary-value problems for fourth-order elliptic equations |
| title_full | Multiple solutions to boundary-value problems for fourth-order elliptic equations |
| title_fullStr | Multiple solutions to boundary-value problems for fourth-order elliptic equations |
| title_full_unstemmed | Multiple solutions to boundary-value problems for fourth-order elliptic equations |
| title_short | Multiple solutions to boundary-value problems for fourth-order elliptic equations |
| title_sort | multiple solutions to boundary-value problems for fourth-order elliptic equations |
| topic_facet | Biharmonic boundary value problems critical points perturbation methods multiple solutions. Primary 35J60; Secondary 35B33 35J25 35J70 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6958 |
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