International Journal of Nonlinear Analysis and Applications
On a class of $l(x)$-biharmonic Kirchhoff-type problem
Document Type : Research Paper
Author
Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran
Abstract
In this paper we deal with the multiplicity of solutions for the following Kirchhoff-type problem with Navier-boundary conditions
\begin{equation*}
\begin{gathered}
\mathcal{K} \Big (\int_{\Lambda}\frac{1}{l(\chi)}|\Delta \varphi|^{l(\chi)}d\chi\Big) \Delta (|\Delta \varphi|^{l(\chi)-2}\Delta \varphi)=\theta |\varphi|^{r(\chi)-2}\varphi +\eta |\varphi|^{t(\chi)-2}\varphi \quad \text{in } \Lambda,\\
\varphi =\Delta \varphi =0 \quad \text{on } \partial\Lambda.
\end{gathered}
\end{equation*}
where $\Lambda$ is a bounded domain in $\mathbb{R}^{N}$ and its boundary $\partial \Lambda$, is smooth , and $\mathcal{K} $ is a continuous Kirchhoff-type function, $l(\chi),r(\chi)$ and $t(\chi)$ are continuous functions on $\overline{\Lambda}$, and $\theta$ and $\eta$ are parameters. We investigate multiple solutions for this equation by using the variational methods.
Keywords
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Articles in Press, Corrected Proof
Available Online from 21 October 2025
- Receive Date: 13 June 2024
- Revise Date: 23 July 2024
- Accept Date: 19 August 2024