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\(p(\cdot )\)-Laplacian problem with nonlinear singular terms

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Abstract

The aim of this article is to study the existence of solution for \(p(\cdot )\)-Laplacian problem with nonlinear singular terms

$$\begin{aligned} -\Delta _{p(x)}u=\frac{f(x)}{u^{\alpha }}, \ in \ \Omega . \end{aligned}$$

Where \(\alpha \ge 1\) and \(p(\cdot )\) is a continuous function defined on \({\bar{\Omega }}\) with \(\Omega\) is a bounded regular domain in \({\mathbb{R}}^{N}, N \ge p(x)> 1\). f is assumed to be a non negative function belonging to a suitable Lebesgue space \(L^{m}(\Omega )\).

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Authors and Affiliations

  1. Labo Math Appli, Faculty of Sciences, B. P. 20, El Jadida, Morocco

    N. Elharrar & H. Talibi

  2. Labo DGTIC, Department of Mathematics, CRMEF Casablanca-Settat, El Jadida, Morocco

    J. Igbida

Authors
  1. N. Elharrar
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  2. J. Igbida
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  3. H. Talibi
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Correspondence to N. Elharrar.

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Elharrar, N., Igbida, J. & Talibi, H. \(p(\cdot )\)-Laplacian problem with nonlinear singular terms. Rend. Circ. Mat. Palermo, II. Ser 71, 105–118 (2022). https://doi.org/10.1007/s12215-021-00604-y

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