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Existence of three weak solutions for an anisotropic quasi-linear elliptic problem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 9، دوره 14، شماره 10، دی 2023، صفحه 85-93 اصل مقاله (399.56 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.30429.4399 | ||
| نویسندگان | ||
| Ahmed Ahmed* 1؛ Mohamed Saad Bouh Elemine Vall2 | ||
| 1Mathematics and Computer Sciences Department, University of Nouakchott, Faculty of Science and Technology, Nouakchott, Mauritania | ||
| 2Department of Mathematics, Professional University Institute, Research unity: Modelling and Scientific Calculus, Nouakchott, Mauritania | ||
| تاریخ دریافت: 02 اردیبهشت 1402، تاریخ بازنگری: 10 اردیبهشت 1402، تاریخ پذیرش: 20 اردیبهشت 1402 | ||
| چکیده | ||
| We consider in this paper a Neumann $\vec{p}(x)-$elliptic problems of the type $$\left\{\begin{array}{ll} - \Delta_{\vec{p}(x)} u+ \lambda(x)|u|^{p_{0}(x)-2}u = \alpha f(x,u)+ \beta g(x,u) \quad &\mbox{in} \quad \Omega, \\ \displaystyle\sum_{i=1}^{N}\Big| \frac{\partial u}{\partial x_{i}}\Big|^{p_{i}(x)-2}\frac{\partial u}{\partial x_{i}}\gamma_{i} =0 \quad &\mbox{on} \quad \partial\Omega.\end{array}\right.$$ We prove the existence of three weak solutions in the framework of anisotropic Sobolev spaces with variable exponent $W^{1,\vec{p}(\cdot)}(\Omega)$ under some hypotheses. The approach is based on a recent three critical points theorem for differentiable functionals. | ||
| کلیدواژهها | ||
| Neumann elliptic problem؛ weak solutions؛ Variational principle؛ Anisotropic variable exponent Sobolev spaces | ||
| مراجع | ||
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