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

سال انتشار: 1404
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 79

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شناسه ملی سند علمی:

JR_IJNAA-16-1_029

تاریخ نمایه سازی: 14 مرداد 1403

چکیده مقاله:

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=۱}^{N}M_{i}\left(\int_{\Omega}\displaystyle\frac{۱}{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)-۲}\frac{\partial u}{\partial x_{i}}\right) = f(x,u) &\mbox{ in } \Omega, \\u =۰ \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.

کلیدواژه ها:

Nonlinear elliptic equations ، Variational methods applied on PDEs ، Positive solutions to PDEs

نویسندگان

Ahmed Ahmed

{Mathematics and Computer Sciences Department, Research Unit Geometry, Algebra, Analysis and Applications, Faculty of Science and Technology, University of Nouakchott, Nouakchott, Mauritania

Mohamed Saad Bouh Elemine Vall

Department of Industrial Engineering and Applied Mathematics, Professional University Institute, University of Nouakchott, Nouakchott, Mauritania

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