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

• Date: 2023
• Main Authors: Luyen, Duong Trong, Trang, Mai Thi Thu
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2023
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6958
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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}^...