Year: 2025
Type: article
Abstract: In this work, we deal with the eigenvalues of the $ p(x) $-triharmonic Navier problem$ \begin{equation*} \begin{gathered} -\Delta^3_{p(x)}u = \lambda |u|^{p(x)-2}u, \quad\quad\quad\text{in }\Omega, \\ \quad\quad \Delta^2u = \Delta u = u = 0, \quad \quad\text{on }\partial \Omega. \end{gathered} \end{equation*} $We establish the existence of infinitely many eigenvalues for the sixth-order problem and investigate their properties. Specifically, we prove that the set of eigenvalues is nonempty and infinite, with the supremum of the eigenvalues being infinity. Additionally, we provide sufficient conditions for the infimum of the eigenvalues to be zero.
Source: Journal of Dynamics and Games
DOI: 10.3934/jdg.2025020
Authors: Abdelhak Bousgheiri, Anass Ourraoui
Institution: Mohamed I University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409772428