Multiplicity analysis of positive weak solutions in a quasi-linear Dirichlet problem inspired by Kirchhoff-type phenomena | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 29، دوره 16، شماره 1، فروردین 2025، صفحه 359-369 اصل مقاله (432.31 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.32433.4823 | ||
| نویسندگان | ||
| Ahmed Ahmed* 1؛ Mohamed Saad Bouh Elemine Vall2 | ||
| 1{Mathematics and Computer Sciences Department, Research Unit Geometry, Algebra, Analysis and Applications, Faculty of Science and Technology, University of Nouakchott, Nouakchott, Mauritania | ||
| 2Department of Industrial Engineering and Applied Mathematics, Professional University Institute, University of Nouakchott, Nouakchott, Mauritania | ||
| چکیده | ||
| The main focus of this paper lies in investigating the existence of infinitely many positive weak solutions for the following elliptic-Kirchhoff equation with Dirichlet boundary condition \begin{equation*} \left\{\begin{array}{ll} -\sum_{i=1}^{N}M_{i}\left(\int_{\Omega}\displaystyle\frac{1}{p_{i}(x)}\displaystyle\Big|\frac{\partial u}{\partial x_{i}}\Big|^{p_{i}(x)}dx\right)\frac{\partial}{\partial x_{i}}\left(\Big|\frac{\partial u}{\partial x_{i}}\Big|^{p_{i}(x)-2} \frac{\partial u}{\partial x_{i}}\right) = f(x,u) &\mbox{ in } \Omega, \\ u =0 \quad &\mbox{on} \quad \partial\Omega.\end{array}\right. \end{equation*} The methodology adopted revolves around the technical approach utilizing the direct variational method within the framework of anisotropic variable exponent Sobolev spaces. | ||
| کلیدواژهها | ||
| Nonlinear elliptic equations؛ Variational methods applied on PDEs؛ Positive solutions to PDEs | ||
| مراجع | ||
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