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 |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865793695406620672 |
|---|---|
| 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_institution_txt_mv | [
{
"author": "Duong Trong Luyen",
"institution": "Department of Mathematics, Hoa Lu University, Ninh Nhat, Ninh Binh City, Vietnam, International Center for Research and Postgraduate Training in Mathematics, Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam"
},
{
"author": "Mai Thi Thu Trang",
"institution": "Department of Basic, Academy of Finance, Duc Thang Wrd., Bac Tu Liem Dist., Hanoi, Vietnam"
}
] |
| 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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