Multiplicity analysis of positive weak solutions in a quasi-linear Dirichlet problem inspired by Kirchhoff-type phenomena

Ahmed, Ahmed; Elemine Vall, Mohamed Saad  Bouh

doi:10.22075/ijnaa.2023.32433.4823

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	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
تاریخ دریافت: 03 آذر 1402، تاریخ پذیرش: 24 آذر 1402
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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Multiplicity analysis of positive weak solutions in a quasi-linear Dirichlet problem inspired by Kirchhoff-type phenomena