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

Duong Trong  Luyen; Mai Thi Thu  Trang

doi:10.37863/umzh.v75i6.6958

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

DOI: https://doi.org/10.37863/umzh.v75i6.6958

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.

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