@Article{JMS-54-337,
author = {Adil and Abbassi and abbassi91@yahoo.fr and 16722 and LMACS Laboratory, Mathematics Department, Faculty of Sciences and Techniques, Sultan Moulay Slimane University Beni-Mellal, BP: 523, Morocco and Adil Abbassi and Chakir and Allalou and chakir.allalou@yahoo.fr and 16721 and LMACS Laboratory, Mathematics Department, Faculty of Sciences and Techniques, Sultan Moulay Slimane University Beni-Mellal, BP: 523, Morocco and Chakir Allalou and Abderrazak and Kassidi and abderrazakassidi@gmail.com and 16767 and LMACS Laboratory, Mathematics Department, Faculty of Sciences and Techniques, Sultan Moulay Slimane University Beni-Mellal, BP: 523, Morocco and Abderrazak Kassidi},
title = {Anisotropic Elliptic Nonlinear Obstacle Problem with Weighted Variable Exponent},
journal = {Journal of Mathematical Study},
year = {2021},
volume = {54},
number = {4},
pages = {337--356},
abstract = {In this paper, we are concerned with a show the existence of a entropy solution to the obstacle problem associated with the equation of the type :

$\begin{cases} Au+g(x,u,∇u) = f & {\rm in} & Ω \\ u=0 & {\rm on} & ∂Ω \end{cases}$

where $\Omega$ is a bounded open subset of $\;\mathbb{R}^{N}$, $N\geq 2$, $A\,$ is an operator of Leray-Lions type acting from $\; W_{0}^{1,\overrightarrow{p}(.)} (\Omega,\ \overrightarrow{w}(.))\;$ into its dual $\; W_{0}^{-1,\overrightarrow{p}'(.)} (\Omega,\ \overrightarrow{w}^*(.))$ and $\,L^1\,-\,$deta. The nonlinear term $\;g\,$: $\Omega\times \mathbb{R}\times \mathbb{R}^{N}\longrightarrow \mathbb{R} $ satisfying only some growth condition.

},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v54n4.21.01},
url = {http://global-sci.org/intro/article_detail/jms/19287.html}
}