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Nonlinear elliptic equations with unbounded coefficient and singular lower order term

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Abstract

In this paper, we are interested in the existence result of solutions for nonlinear and singular Dirichlet problem whose model is

$$\begin{aligned} \left\{ \begin{aligned}&-\mathrm{div}\Big (b(u) \nabla u\Big )+\mu (x) \frac{|\nabla u|^2}{|u|^\theta } \mathrm{{sign}}(u)=f\ \ \mathrm{in}\ \Omega ,\\&u=0\ \ \mathrm{on}\ {\partial \Omega },\\ \end{aligned} \right. \end{aligned}$$

where \(\Omega \) is a bounded open subset of \(\mathbb {R}^N (N\ge 2)\), b(s) is a positive continuous function which blows up for a finite value of the unknown, \(\mu (x)\) is positive, bounded and measurable, \(0<\theta < 1\), and the source f belongs to \(L^1(\Omega )\).

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Acknowledgements

The authors would like to express sincere thanks to the anonymous referee for his valuable comments and suggestions that improve the manuscript.

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Authors and Affiliations

  1. Faculté des Sciences et Techniques, Université Hassan 1, B.P. 764, Settat, Morocco

    Amine Marah & Khaled Zaki

  2. Faculté des Sciences Juridiques, Économiques et Sociales, Université Hassan 1, B.P. 764, Settat, Morocco

    Hicham Redwane

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  1. Amine Marah
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  2. Hicham Redwane
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Correspondence to Amine Marah.

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Marah, A., Redwane, H. & Zaki, K. Nonlinear elliptic equations with unbounded coefficient and singular lower order term. J. Fixed Point Theory Appl. 22, 68 (2020). https://doi.org/10.1007/s11784-020-00804-6

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