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Existence of bounded solutions for a class of singular elliptic problems involving the 1-Laplacian operator

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Abstract

In this work we study existence and regularity of solutions to problems which are modeled by

$$\begin{aligned} \left\{ \begin{array}{ll} -\Delta _{p}u+u \vert \nabla u \vert ^{p}=fh(u) &{} \hbox {in } \Omega , \\ u=0 &{} \hbox {on } \partial \Omega . \end{array} \right. \end{aligned}$$

Here \( \Omega \) is an open bounded subset of \(\mathbb {R}^{N}\) \((N \ge 2)\) with Lipschitz boundary, \( \Delta _{p}u:=\text{ div }(\vert \nabla u\vert ^{p-2}\nabla u) (1\le p<N)\) is the p-Laplacian operator, \( f\in L^{q}(\Omega )\) \( (q>\frac{N}{p})\) is a nonnegative function and h is a continuous real function that may possibly blow up at zero.

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  1. Laboratory LIPIM, National School of Applied Sciences Khouribga, Sultan Moulay Slimane University, 25000, Khouribga, Morocco

    Mohamed El Hichami & Youssef El Hadfi

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  1. Mohamed El Hichami
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  2. Youssef El Hadfi
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El Hichami, M., El Hadfi, Y. Existence of bounded solutions for a class of singular elliptic problems involving the 1-Laplacian operator. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 111 (2023). https://doi.org/10.1007/s13398-023-01444-4

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