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Existence of entropy solutions for anisotropic quasilinear degenerated elliptic problems with Hardy potential

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Abstract

The aim of this work is to give an existence result of entropy solutions for anisotropic quasilinear degenerated elliptic problems of the form

$$\begin{aligned} -\text{ div } (a(x,u,\nabla u)) + |u|^{s-1}u= f +\rho \frac{|u|^{p_{0}-2}u}{|x|^{p_{0}}}, \quad \text{ in } \ \ \varOmega , \end{aligned}$$

where \(-\text{ div } (a(x,u,\nabla u))\) is a Leray-Lions operator from \(W_{0}^{1,(p_{i})}(\varOmega ,w)\) to its dual, \(\varOmega \) is an open bounded subset of \(I\!\!R^{N}\) \((N\ge 2)\) containing the origin, the datum f is assumed to be merely integrable and \(\rho \) is a positive constant.

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Acknowledgements

The authors thank the referees for their constructive comments and suggestions that helped improving the original manuscript.

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Authors and Affiliations

  1. Laboratoire d’Analyse Mathématique et Applications (LAMA), Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, BP 1796, Atlas Fès, Morocco

    Elhoussine Azroul, Mohammed Bouziani & Abdelkrim Barbara

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  1. Elhoussine Azroul
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  2. Mohammed Bouziani
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  3. Abdelkrim Barbara
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Correspondence to Mohammed Bouziani.

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Azroul, E., Bouziani, M. & Barbara, A. Existence of entropy solutions for anisotropic quasilinear degenerated elliptic problems with Hardy potential. SeMA 78, 475–499 (2021). https://doi.org/10.1007/s40324-021-00247-0

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