Multiplicity of solutions for a singular problem involving the fractional p$p$‐Laplacian in the whole space

Zijian Wu and Haibo Chen

Mathematische Nachrichten, 2024, vol. 297, issue 4, 1483-1500

Abstract: In this paper, we prove the multiplicity of positive solutions for the following singular problem involving the fractional p$p$‐Laplacian: (−Δ)psu+V(x)|u|p−2u=a(x)uκ−1+μb(x)uq−1,inRN$$\begin{equation*} \hspace*{4pc}(-\Delta )_p^su+V(x)|u|^{p-2}u=a(x)u^{\kappa -1}+\mu b(x)u^{q-1}, \mbox{ in } \mathbb {R}^N \end{equation*}$$u(x)>0,inRN.$$\begin{equation*} \hspace*{10.6pc}u(x)>0, \mbox{ in } \mathbb {R}^N. \end{equation*}$$Here, μ>0$\mu >0$, 0

Date: 2024
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