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Existence of three solutions for fourth-order Kirchhoff type elliptic problems with Hardy potential | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 2، دوره 15، شماره 5، مرداد 2024، صفحه 11-22 اصل مقاله (430.51 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29983.4304 | ||
| نویسندگان | ||
| Mostafa Negravi* 1؛ Ghasem Afrouzi2 | ||
| 1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran | ||
| 2Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran | ||
| تاریخ دریافت: 30 بهمن 1401، تاریخ پذیرش: 08 اردیبهشت 1402 | ||
| چکیده | ||
| In this work, we establish existence results for the following fourth-order Kirchhoff-type elliptic problem with Hardy potential \begin{equation*} \begin{gathered} M \Big(\int_{\Omega} |\Delta u|^p dx\Big) \Delta_p^2 u - \frac{a}{|x|^{p}} |u|^{p-2} u = \lambda f(x, u), \quad \text{in } \Omega, \\ u = \Delta u = 0, \quad \text{on } \partial \Omega. \end{gathered} \end{equation*} Precisely, by using the classical Hardy inequality and critical point theory, we prove the existence of multiple weak solutions for the fourth-order Kirchhoff-type elliptic problem with Hardy potential. | ||
| کلیدواژهها | ||
| Kirchhoff-type؛ Multiple solutions؛ Critical points theory؛ Hardy potential؛ $p$-biharmonic type operator | ||
| مراجع | ||
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