Multiple solutions to boundary-value problems for fourth-order elliptic equations

  • Duong Trong Luyen 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
  • Mai Thi Thu Trang Department of Basic, Academy of Finance, Duc Thang Wrd., Bac Tu Liem Dist., Hanoi, Vietnam

Анотація

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.

Посилання

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Опубліковано
20.06.2023
Як цитувати
LuyenD. T., і TrangM. T. T. «Multiple Solutions to Boundary-Value Problems for Fourth-Order Elliptic Equations». Український математичний журнал, вип. 75, вип. 6, Червень 2023, с. 830 -41, doi:10.37863/umzh.v75i6.6958.
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