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On a class of $l(x)$-biharmonic Kirchhoff-type problem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 29 مهر 1404 اصل مقاله (384.96 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.34439.5145 | ||
| نویسنده | ||
| Maryam Mirzapour* | ||
| Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran | ||
| تاریخ دریافت: 24 خرداد 1403، تاریخ بازنگری: 02 مرداد 1403، تاریخ پذیرش: 29 مرداد 1403 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Kirchhoff type problem؛ Fourth-order operator؛ Variable exponent؛ Critical points؛ Variational methods | ||
| مراجع | ||
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