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
Keywords: Biharmonic, boundary value problems, critical points, perturbation methods, multiple solutions.

Abstract

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.

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Published
20.06.2023
How to Cite
LuyenD. T., and TrangM. T. T. “Multiple Solutions to Boundary-Value Problems for Fourth-Order Elliptic Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 6, June 2023, pp. 830 -41, doi:10.37863/umzh.v75i6.6958.
Section
Research articles